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

样章
作者：
R. A. Bailey, Peter J. Cameron，Yaokun Wu 主编
定价：
169.00元
ISBN：
978-7-04-065095-2
版面字数：
520.00千字
开本：
特殊
全书页数：
暂无
装帧形式：
平装
重点项目：
暂无
出版时间：
2025-10-24
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
暂无
  • 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
      • 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
      • 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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