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群与图，设计与动力学 （英文版）Groups and Graphs, Designs and Dynamics

暂无简介
作者：
R. A. Bailey, Peter J. Cameron，Yaokun Wu 主编
定价：
169.00 元
出版时间：
2025-10-24
ISBN：
978-7-04-065095-2
物料号：
65095-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
拓扑学
重点项目：
暂无
版面字数：
520千字
开本：
特殊
装帧形式：
平装
页数：
暂无
最新
印次时间：
2025年01月
  • 目录
    • 前辅文
      • 1 Topics in representation theory of finite groups T. Ceccherini-Silberstein, F. Scarabotti and F. Tolli
        • 1.1 Introduction
          • 1.2 Representation theory and harmonic analysis on finite groups
            • 1.2.1 Representations
              • 1.2.2 Finite Gelfand pairs
                • 1.2.3 Spherical functions
                  • 1.2.4 Harmonic analysis of finite Gelfand pairs
                  • 1.3 Laplace operators and spectra of random walks on finite graphs
                    • 1.3.1 Finite graphs and their spectra
                      • 1.3.2 Strongly regular graphs
                      • 1.4 Association schemes
                        • 1.5 Applications of Gelfand pairs to probability
                          • 1.5.1 Markov chains
                            • 1.5.2 The Ehrenfest diffusion model
                            • 1.6 Induced representations and Mackey theory
                              • 1.6.1 Induced representations
                                • 1.6.2 Mackey theory
                                  • 1.6.3 The little group method of Mackey and Wigner
                                    • 1.6.4 Hecke algebras
                                      • 1.6.5 Multiplicity-free triples and their spherical functions
                                      • 1.7 Representation theory of GL(2;Fq)
                                        • 1.7.1 Finite fields and their characters
                                          • 1.7.2 Representation theory of the affine group Aff(Fq)
                                            • 1.7.3 The general linear group GL(2,Fq)
                                              • 1.7.4 Representations of GL(2,Fq)
                                              • References
                                              • 2 Quantum probability approach to spectral analysis of growing graphs N. Obata
                                                • 2.1 Introduction
                                                  • 2.2 Basic concepts of quantum probability
                                                    • 2.2.1 Algebraic probability spaces
                                                      • 2.2.2 Spectral distributions
                                                        • 2.2.3 Convergence of random variables
                                                          • 2.2.4 Classical probability vs quantum probability
                                                            • 2.2.5 Notes
                                                            • 2.3 Quantum decomposition
                                                              • 2.3.1 Jacobi coefficients and interacting Fock spaces
                                                                • 2.3.2 Orthogonal polynomials
                                                                  • 2.3.3 Quantum decomposition
                                                                    • 2.3.4 How to explicitly compute μ from ({ωn},{αn})
                                                                      • 2.3.5 Boson, fermion and free Fock spaces
                                                                        • 2.3.6 Notes
                                                                        • 2.4 Spectral distributions of graphs
                                                                          • 2.4.1 Adjacency matrix as a real random variable
                                                                            • 2.4.2 IFS structure associated to graphs
                                                                              • 2.4.3 Homogeneous trees and Kesten distributions
                                                                              • 2.5 Growing graphs
                                                                                • 2.5.1 Formulation of question in general
                                                                                  • 2.5.2 Growing distance-regular graphs
                                                                                    • 2.5.3 Growing regular graphs
                                                                                      • 2.5.4 Notes
                                                                                      • 2.6 Concepts of independence and graph products
                                                                                        • 2.6.1 From classical to commutative independence
                                                                                          • 2.6.2 Graph products
                                                                                            • 2.6.3 Central Limit Theorem for Cartesian powers
                                                                                              • 2.6.4 Monotone independence and comb product
                                                                                                • 2.6.5 Boolean independence and star product
                                                                                                  • 2.6.6 Convolutions of spectral distributions
                                                                                                    • 2.6.7 Notes
                                                                                                    • References
                                                                                                    • 3 Laplacian eigenvalues and optimality R. A. Bailey and P. J. Cameron
                                                                                                      • 3.1 Block designs in experiments
                                                                                                        • 3.1.1 Experiments in blocks
                                                                                                          • 3.1.2 Complete-block designs
                                                                                                            • 3.1.3 Incomplete-block designs
                                                                                                              • 3.1.4 Matrix formulae
                                                                                                                • 3.1.5 Eigenspaces of real symmetric matrices
                                                                                                                  • 3.1.6 Fisher’s Inequality
                                                                                                                    • 3.1.7 Constructions
                                                                                                                      • 3.1.8 Partially balanced designs
                                                                                                                        • 3.1.9 Laplacian matrix and information matrix
                                                                                                                          • 3.1.10 Estimation and variance
                                                                                                                            • 3.1.11 Reparametrization
                                                                                                                              • 3.1.12 Exercises
                                                                                                                              • 3.2 Laplacian matrices and their eigenvalues
                                                                                                                                • 3.2.1 Which graph is best?
                                                                                                                                  • 3.2.2 Graph terminology
                                                                                                                                    • 3.2.3 The Laplacian of a graph
                                                                                                                                      • 3.2.4 Isoperimetric number
                                                                                                                                        • 3.2.5 Signed incidence matrix
                                                                                                                                          • 3.2.6 Generalized inverse; Moore–Penrose inverse
                                                                                                                                            • 3.2.7 Electrical networks
                                                                                                                                              • 3.2.8 The Matrix-Tree Theorem
                                                                                                                                                • 3.2.9 Markov chains
                                                                                                                                                  • 3.2.10 Exercises
                                                                                                                                                  • 3.3 Designs, graphs and optimality
                                                                                                                                                    • 3.3.1 Two graphs associated with a block design
                                                                                                                                                      • 3.3.2 Laplacian matrices
                                                                                                                                                        • 3.3.3 Estimation and variance
                                                                                                                                                          • 3.3.4 Resistance distance
                                                                                                                                                            • 3.3.5 Spanning trees
                                                                                                                                                              • 3.3.6 Measures of optimality
                                                                                                                                                                • 3.3.7 Some optimal designs
                                                                                                                                                                  • 3.3.8 Designs with very low replication
                                                                                                                                                                    • 3.3.9 Exercises
                                                                                                                                                                    • 3.4 Further topics
                                                                                                                                                                      • 3.4.1 Sylvester designs
                                                                                                                                                                        • 3.4.2 Sparse versus dense
                                                                                                                                                                          • 3.4.3 Variance-balanced designs
                                                                                                                                                                            • 3.4.4 Recognising a concurrence graph
                                                                                                                                                                              • 3.4.5 Other graph parameters
                                                                                                                                                                                • 3.4.6 Some open problems
                                                                                                                                                                                  • 3.4.7 Exercises
                                                                                                                                                                                  • References
                                                                                                                                                                                  • 4 Symbolic dynamics and the stable algebra of matrices M. Boyle and S. Schmieding
                                                                                                                                                                                    • 4.1 Overview
                                                                                                                                                                                      • 4.2 Basics
                                                                                                                                                                                        • 4.2.1 Topological dynamics
                                                                                                                                                                                          • 4.2.2 Symbolic dynamics
                                                                                                                                                                                            • 4.2.3 Edge SFTs
                                                                                                                                                                                              • 4.2.4 The continuous shift-commuting maps
                                                                                                                                                                                                • 4.2.5 Powers of an edge SFT
                                                                                                                                                                                                  • 4.2.6 Periodic points and nonzero spectrum
                                                                                                                                                                                                    • 4.2.7 Classification of SFTs
                                                                                                                                                                                                      • 4.2.8 Strong shift equivalence of matrices, classification of SFTs
                                                                                                                                                                                                        • 4.2.9 Shift equivalence
                                                                                                                                                                                                          • 4.2.10 Williams’ shift equivalence conjecture
                                                                                                                                                                                                            • 4.2.11 Appendix 2
                                                                                                                                                                                                            • 4.3 Shift equivalence and strong shift equivalence over a ring
                                                                                                                                                                                                              • 4.3.1 SE-Z+: dynamical meaning and reduction to SE-Z
                                                                                                                                                                                                                • 4.3.2 Strong shift equivalence of matrices over a ring
                                                                                                                                                                                                                  • 4.3.3 SE, SSE and det(I−tA)
                                                                                                                                                                                                                    • 4.3.4 Shift equivalence over a ring R
                                                                                                                                                                                                                      • 4.3.5 SIM-Z and SE-Z: some example classes
                                                                                                                                                                                                                        • 4.3.6 SE-Z via direct limits
                                                                                                                                                                                                                          • 4.3.7 SE-Z via polynomials
                                                                                                                                                                                                                            • 4.3.8 Cokernel of (I−tA), a Z[t]-module
                                                                                                                                                                                                                              • 4.3.9 Other rings for other systems
                                                                                                                                                                                                                                • 4.3.10 The module-theoretic formulation of SE over a ring
                                                                                                                                                                                                                                  • 4.3.11 Appendix 3
                                                                                                                                                                                                                                  • 4.4 Polynomial matrices
                                                                                                                                                                                                                                    • 4.4.1 Background
                                                                                                                                                                                                                                      • 4.4.2 Presenting SFTs with polynomial matrices
                                                                                                                                                                                                                                        • 4.4.3 Algebraic invariants in the polynomial setting
                                                                                                                                                                                                                                          • 4.4.4 Polynomial matrices: from elementary equivalence to conjugate SFTs
                                                                                                                                                                                                                                            • 4.4.5 Classification of SFTs by positive equivalence in I−NZC
                                                                                                                                                                                                                                              • 4.4.6 Functoriality: flow equivalence in the polynomial setting
                                                                                                                                                                                                                                                • 4.4.7 Appendix 4
                                                                                                                                                                                                                                                • 4.5 Inverse problems for nonnegative matrices
                                                                                                                                                                                                                                                  • 4.5.1 The NIEP
                                                                                                                                                                                                                                                    • 4.5.2 Stable variants of the NIEP
                                                                                                                                                                                                                                                      • 4.5.3 Primitive matrices
                                                                                                                                                                                                                                                        • 4.5.4 Irreducible matrices
                                                                                                                                                                                                                                                          • 4.5.5 Nonnegative matrices
                                                                                                                                                                                                                                                            • 4.5.6 The Spectral Conjecture
                                                                                                                                                                                                                                                              • 4.5.7 Boyle–Handelman Theorem
                                                                                                                                                                                                                                                                • 4.5.8 The Kim–Ormes–Roush Theorem
                                                                                                                                                                                                                                                                  • 4.5.9 Status of the Spectral Conjecture
                                                                                                                                                                                                                                                                    • 4.5.10 Laffey’s Theorem
                                                                                                                                                                                                                                                                      • 4.5.11 The Generalized Spectral Conjectures
                                                                                                                                                                                                                                                                        • 4.5.12 Appendix 5
                                                                                                                                                                                                                                                                        • 4.6 A brief introduction to algebraic K-theory
                                                                                                                                                                                                                                                                          • 4.6.1 K1 of a ring R
                                                                                                                                                                                                                                                                            • 4.6.2 NK1(R)
                                                                                                                                                                                                                                                                              • 4.6.3 Nil0(R)
                                                                                                                                                                                                                                                                                • 4.6.4 K2 of a ring R
                                                                                                                                                                                                                                                                                  • 4.6.5 Appendix 6
                                                                                                                                                                                                                                                                                  • 4.7 The algebraic K-theoretic characterization of the refinement of strong shift equivalence over a ring by shift equivalence
                                                                                                                                                                                                                                                                                    • 4.7.1 Comparing shift equivalence and strong shift equivalence over a ring
                                                                                                                                                                                                                                                                                      • 4.7.2 The Algebraic Shift Equivalence Problem
                                                                                                                                                                                                                                                                                        • 4.7.3 Strong shift equivalence and elementary equivalence
                                                                                                                                                                                                                                                                                          • 4.7.4 The refinement of shift equivalence over a ring by strong shift equivalence
                                                                                                                                                                                                                                                                                            • 4.7.5 The SE and SSE relations in the context of endomorphisms
                                                                                                                                                                                                                                                                                              • 4.7.6 Appendix 7
                                                                                                                                                                                                                                                                                              • 4.8 Automorphisms of SFTs
                                                                                                                                                                                                                                                                                                • 4.8.1 Simple automorphisms
                                                                                                                                                                                                                                                                                                  • 4.8.2 The center of Aut(σA)
                                                                                                                                                                                                                                                                                                    • 4.8.3 Representations of Aut(σA)
                                                                                                                                                                                                                                                                                                      • 4.8.4 Dimension representation
                                                                                                                                                                                                                                                                                                        • 4.8.5 Periodic point representation
                                                                                                                                                                                                                                                                                                          • 4.8.6 Inerts and the sign-gyration compatibility condition
                                                                                                                                                                                                                                                                                                            • 4.8.7 Actions on finite subsystems
                                                                                                                                                                                                                                                                                                              • 4.8.8 Notable problems regarding Aut(σA)
                                                                                                                                                                                                                                                                                                                • 4.8.9 The stabilized automorphism group
                                                                                                                                                                                                                                                                                                                  • 4.8.10 Mapping class groups of subshifts
                                                                                                                                                                                                                                                                                                                    • 4.8.11 Appendix 8
                                                                                                                                                                                                                                                                                                                    • 4.9 Wagoner’s strong shift equivalence complex, and applications
                                                                                                                                                                                                                                                                                                                      • 4.9.1 Wagoner’s SSE complexes
                                                                                                                                                                                                                                                                                                                        • 4.9.2 Homotopy groups for Wagoner’s complexes and Aut(σA)
                                                                                                                                                                                                                                                                                                                          • 4.9.3 Counterexamples to Williams’ conjecture
                                                                                                                                                                                                                                                                                                                            • 4.9.4 Kim–Roush relative sign-gyration method
                                                                                                                                                                                                                                                                                                                              • 4.9.5 Wagoner’s K2-valued obstruction map
                                                                                                                                                                                                                                                                                                                                • 4.9.6 Some remarks and open problems
                                                                                                                                                                                                                                                                                                                                  • 4.9.7 Appendix 9
                                                                                                                                                                                                                                                                                                                                • References
                                                                                                                                                                                                                                                                                                                                  • Subject Index
                                                                                                                                                                                                                                                                                                                                    • Author Index

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