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1.

図書

図書
Jacobus H. van Lint
出版情報: Berlin : Springer-Verlag, 1971  vi, 136 p. ; 26 cm
シリーズ名: Lecture notes in mathematics ; v. 201
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2.

図書

図書
Jacobus H. van Lint
出版情報: Berlin ; New York : Springer-Verlag, 1974  vi, 131 p ; 25 cm
シリーズ名: Lecture notes in mathematics ; 382
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3.

図書

図書
P.J. Cameron and J.H. van Lint
出版情報: Cambridge : Cambridge University Press, 1991  viii, 240 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 22
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Contents
Preface
Notation and terminology
Design theory / 1.:
Strongly regular graphs / 2.:
Graphs with least eigenvalue-2 / 3.:
Regular two-graphs / 4.:
Quasi-symmetric designs / 5.:
A property of the number six / 6.:
Partial geometries / 7.:
Graphs with no triangles / 8.:
Codes / 9.:
Cyclic codes / 10.:
The Golay codes / 11.:
Reed-Muller and Kerdock codes / 12.:
Self-orthogonal codes and projective planes / 13.:
Quadratic residue codes and the Assmus-Mattson Theorem / 14.:
Symmetry codes over F[subscript 3] / 15.:
Nearly perfect binary codes and uniformly packed codes / 16.:
Association schemes / 17.:
References
Index
List of Authors
Contents
Preface
Notation and terminology
4.

図書

図書
J.H. van Lint
出版情報: Berlin ; New York : Springer-Verlag, c1992  xi, 183 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 86
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Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Mathematical Background
Shannon's Theorem
Linear Codes
Some Good Codes
Bounds on Codes
Cyclic Codes
Perfect Codes and Uniformly Packed Codes
Codes over Z(4)
Goppa Codes
Algebraic Geometry Codes
Asymptotically Good Algebraic Codes
Arithmetic Codes
Convolutional Codes
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
5.

図書

図書
edited by M. Hall, Jr. and J. H. Van Lint
出版情報: Dordrecht, Holland : D. Reidel, c1975  viii, 482 p. ; 25 cm
シリーズ名: NATO advanced study institutes series ; ser. C . Mathematical and physical sciences ; v. 16
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6.

図書

図書
J.H. van Lint
出版情報: Berlin : Springer, c1999  xiv, 227 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 86
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Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Mathematical Background
Shannon's Theorem
Linear Codes
Some Good Codes
Bounds on Codes
Cyclic Codes
Perfect Codes and Uniformly Packed Codes
Codes over Z(4)
Goppa Codes
Algebraic Geometry Codes
Asymptotically Good Algebraic Codes
Arithmetic Codes
Convolutional Codes
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
7.

図書

図書
J.H. van Lint and R.M. Wilson
出版情報: Cambridge ; New York : Cambridge University Press, c1992  xii, 530 p. ; 26 cm
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Preface
Graphs / 1.:
Terminology of graphs and digraphs
Eulerian circuits
Hamiltonian circuits
Trees / 2.:
Cayley's theorem
Spanning trees and the greedy algorithm
Colorings of graphs and Ramsey's theorem / 3.:
Brooks' theorem
Ramsey's theorem and Ramsey numbers
The Erdos-Szekeres theorem
Turan's theorem and extremal graphs / 4.:
Turan's theorem and extremal graph theory
Systems of distinct representatives / 5.:
Bipartite graphs
P. Hall's condition
SDRs
Konig's theorem
Birkhoff's theorem
Dilworth's theorem and extremal set theory / 6.:
Partially ordered sets
Dilworth's theorem
Sperner's theorem
Symmetric chains
The Erdos-Ko-Rado theorem
Flows in networks / 7.:
The Ford-Fulkerson theorem
The integrality theorem
Ageneralization of Birkhoff's theorem
De Bruijn sequences / 8.:
The number of De Bruijn sequences
The addressing problem for graphs / 9.:
Quadratic forms
Winkler's theorem
The principle of inclusion and exclusion; inversion formulae / 10.:
Inclusion-exclusion
Derangements
Euler indicator
Mobius function
Mobius inversion
Burnside's lemma
Probleme des menages
Permanents / 11.:
Bounds on permanents
Schrijver's proof of the Minc conjecture
Fekete's lemma
Permanents of doubly stochastic matrices
The Van der Waerden conjecture / 12.:
The early results of Marcus and Newman
London's theorem
Egoritsjev's proof
Elementary counting; Stirling numbers / 13.:
Stirling numbers of the first and second kind
Bell numbers
Generating functions
Recursions and generating functions / 14.:
Elementary recurrences
Catalan numbers
Counting of trees
Joyal theory
Lagrange inversion
Partitions / 15.:
The function Pk(n)
The partition function
Ferrers diagrams
Euler's identity
Asymptotics
The Jacobi triple product identity
Young tableaux and the hook formula
(0,1)-Matrices / 16.:
Matrices with given line sums
Counting (0,1)-matrices
Latin squares / 17.:
Orthogonal arrays
Conjugates and isomorphism
Partial and incomplete latin squares
Counting Latin squares
The Evans conjecture
Hadamard matrices, Reed-Muller codes / 18.:
Hadamard matrices and conference matrices
Recursive constructions
Paley matrices
Williamson's method
Excess of a Hadamard matrix
First order Reed-Muller codes
Designs / 19.:
The Erdos-De Bruijn theorem
Steiner systems
Balanced incomplete block designs
Hadamard designs
Counting, (higher) incidence matrices
The Wilson-Petrenjuk theorem
Symmetric designs
Projective planes
Derived and residual designs
The Bruck-Ryser-Chowla theorem
Constructions of Steiner triple systems
Write-once memories
Codes and designs / 20.:
Terminology of coding theory
The Hamming bound
The Singleton bound
Weight enumerators and MacWilliams' theorem
The Assmus-Mattson theorem
Symmetry codes
The Golay codes
Codes from projective planes
Strongly regular graphs and partial geometries / 21.:
The Bose-Mesner algebra
Eigenvalues
The integrality condition
Quasisymmetric designs
The Krein condition
The absolute bound
Uniqueness theorems
Partial geometries
Examples
Orthogonal Latin squares / 22.:
Pairwise orthogonal Latin squares and nets
Euler's conjecture
The Bose-Parker-Shrikhande theorem
Asymptotic existence
Orthogonal arrays and transversal designs
Dlifference methods, orthogonal subsquares
Projective and combinatorial geometries / 23.:
Projective and affine geometries
Quality
Pasch's axiom
Desargues' theorem
Combinatorial geometries
Geometric lattices
Greene's theorem
Gaussian numbers and q-analogues / 24.:
Chains in the lattice of subspaces, q-analogue of Sperner's theorem
Interpretation of the coefficients of the Gaussian polynomials
Spreads
Lattices and Mobius inversion / 25.:
The incidence algebra of a poset
The Mobius function, chromatic polynomial of a graph
Weisner's theorem
Complementing permutations of geometric lattices
Connected labeled graphs
Combinatorial designs and projective geometries / 26.:
Arcs and subplanes in projective planes
Blocking sets
Quadratic and Hermitian forms
Unitals
Generalized quadrangles
Mobius planes
Difference sets and automorphisms / 27.:
Automorphisms of symmetric designs
Paley-Todd and Stanton-Sprott difference sets
Singer's theorem
Difference sets and the group ring / 28.:
The Multiplier Theorem and extensions
Homomorphisms and further necessary conditions
Codes and symmetric designs / 29.:
The sequence of codes of a symmetric design
Wilbrink's theorem
Association schemes / 30.:
Examples, the eigenmatrices and orthogonality relations
Formal duality, the distribution vector of a subset
Delsarte's inequalities
Polynomial schemes
Perfect codes and tight designs
Algebraic graph theory: eigenvalue techniques / 31.:
Tournaments and the Graham-Pollak theorem
The spectrum of a graph
Hoffman's theorem
Shannon capacity
Applications of interlacing and Perron-Frobenius
Graphs: planarity and duality / 32.:
Deletion and contraction
The chromatic polynomial, Euler's formula
Whitney duality, matroids
Graphs: colorings and embeddings / 33.:
The Five Color Theorem, embeddings and colorings on arbitrary surfaces
The Heawood conjecture
The Edmonds embedding technique
Electrical networks and squared squares / 34.:
The matrix-tree theorem
The network of a squared rectangle
Kirchhoff's theorem
Polya theory of counting / 35.:
The cycle index of a permutation group
Counting orbits
Weights, necklaces, the symmetric group
Stirling numbers
Baranyai's theorem / 36.:
One-factorizations of complete graphs and complete designs
Hints and comments on problems / Appendix 1.:
Hints
Suggestions
Comments on the problems in each chapter
Formal power series / Appendix 2.:
Formal power series ring, formal derivatives
Inverse functions
Residues
The Lagrange-Burmann formula
Name Index
Subject Index
Preface
Graphs / 1.:
Terminology of graphs and digraphs
8.

図書

図書
J. H. ヴァン・リント, R. M. ウィルソン著 ; 澤正憲, 萩田真理子訳
出版情報: 東京 : 丸善出版, 2018.3-2019.10  2冊 ; 21cm
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強正則グラフと偏均衡幾何
直交ラテン方格
射影幾何と組合せ幾何
ガウスの二項係数とq‐類似
束とメビウスの反転公式
組合せデザインと射影幾何
差集合と自己同型写像
差集合と群環
符号と対称デザイン
アソシエーションスキーム
代数的グラフ理論
グラフの連結度
平面グラフと彩色
Whitney双対
グラフの埋め込み
電気回路と正方形の正方形分割
数え上げに関するポリアの理論
Baranyaiの定理
付録 : 問題のヒントとコメント
グラフ
ラベル付き木と数え上げ
グラフの彩色とRamsey理論
Tur : ́anの定理と極値グラフ
個別代表系
Dilworthの定理と極値集合論
ネットワークフロー
De : Bruijn系列
(0,1,*)問題:グラフのアドレッシングとハッシュコーディング
包除原理と反転公式〔ほか〕
強正則グラフと偏均衡幾何
直交ラテン方格
射影幾何と組合せ幾何
9.

図書

図書
J.H. van Lint and R.M. Wilson
出版情報: Cambridge ; New York : Cambridge University Press, 2001  xiv, 602 p. ; 26 cm
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目次情報: 続きを見る
Preface
Graphs / 1.:
Terminology of graphs and digraphs
Eulerian circuits
Hamiltonian circuits
Trees / 2.:
Cayley's theorem
Spanning trees and the greedy algorithm
Colorings of graphs and Ramsey's theorem / 3.:
Brooks' theorem
Ramsey's theorem and Ramsey numbers
The Erdos-Szekeres theorem
Turan's theorem and extremal graphs / 4.:
Turan's theorem and extremal graph theory
Systems of distinct representatives / 5.:
Bipartite graphs
P. Hall's condition
SDRs
Konig's theorem
Birkhoff's theorem
Dilworth's theorem and extremal set theory / 6.:
Partially ordered sets
Dilworth's theorem
Sperner's theorem
Symmetric chains
The Erdos-Ko-Rado theorem
Flows in networks / 7.:
The Ford-Fulkerson theorem
The integrality theorem
Ageneralization of Birkhoff's theorem
De Bruijn sequences / 8.:
The number of De Bruijn sequences
The addressing problem for graphs / 9.:
Quadratic forms
Winkler's theorem
The principle of inclusion and exclusion; inversion formulae / 10.:
Inclusion-exclusion
Derangements
Euler indicator
Mobius function
Mobius inversion
Burnside's lemma
Probleme des menages
Permanents / 11.:
Bounds on permanents
Schrijver's proof of the Minc conjecture
Fekete's lemma
Permanents of doubly stochastic matrices
The Van der Waerden conjecture / 12.:
The early results of Marcus and Newman
London's theorem
Egoritsjev's proof
Elementary counting; Stirling numbers / 13.:
Stirling numbers of the first and second kind
Bell numbers
Generating functions
Recursions and generating functions / 14.:
Elementary recurrences
Catalan numbers
Counting of trees
Joyal theory
Lagrange inversion
Partitions / 15.:
The function Pk(n)
The partition function
Ferrers diagrams
Euler's identity
Asymptotics
The Jacobi triple product identity
Young tableaux and the hook formula
(0,1)-Matrices / 16.:
Matrices with given line sums
Counting (0,1)-matrices
Latin squares / 17.:
Orthogonal arrays
Conjugates and isomorphism
Partial and incomplete latin squares
Counting Latin squares
The Evans conjecture
Hadamard matrices, Reed-Muller codes / 18.:
Hadamard matrices and conference matrices
Recursive constructions
Paley matrices
Williamson's method
Excess of a Hadamard matrix
First order Reed-Muller codes
Designs / 19.:
The Erdos-De Bruijn theorem
Steiner systems
Balanced incomplete block designs
Hadamard designs
Counting, (higher) incidence matrices
The Wilson-Petrenjuk theorem
Symmetric designs
Projective planes
Derived and residual designs
The Bruck-Ryser-Chowla theorem
Constructions of Steiner triple systems
Write-once memories
Codes and designs / 20.:
Terminology of coding theory
The Hamming bound
The Singleton bound
Weight enumerators and MacWilliams' theorem
The Assmus-Mattson theorem
Symmetry codes
The Golay codes
Codes from projective planes
Strongly regular graphs and partial geometries / 21.:
The Bose-Mesner algebra
Eigenvalues
The integrality condition
Quasisymmetric designs
The Krein condition
The absolute bound
Uniqueness theorems
Partial geometries
Examples
Orthogonal Latin squares / 22.:
Pairwise orthogonal Latin squares and nets
Euler's conjecture
The Bose-Parker-Shrikhande theorem
Asymptotic existence
Orthogonal arrays and transversal designs
Dlifference methods, orthogonal subsquares
Projective and combinatorial geometries / 23.:
Projective and affine geometries
Quality
Pasch's axiom
Desargues' theorem
Combinatorial geometries
Geometric lattices
Greene's theorem
Gaussian numbers and q-analogues / 24.:
Chains in the lattice of subspaces, q-analogue of Sperner's theorem
Interpretation of the coefficients of the Gaussian polynomials
Spreads
Lattices and Mobius inversion / 25.:
The incidence algebra of a poset
The Mobius function, chromatic polynomial of a graph
Weisner's theorem
Complementing permutations of geometric lattices
Connected labeled graphs
Combinatorial designs and projective geometries / 26.:
Arcs and subplanes in projective planes
Blocking sets
Quadratic and Hermitian forms
Unitals
Generalized quadrangles
Mobius planes
Difference sets and automorphisms / 27.:
Automorphisms of symmetric designs
Paley-Todd and Stanton-Sprott difference sets
Singer's theorem
Difference sets and the group ring / 28.:
The Multiplier Theorem and extensions
Homomorphisms and further necessary conditions
Codes and symmetric designs / 29.:
The sequence of codes of a symmetric design
Wilbrink's theorem
Association schemes / 30.:
Examples, the eigenmatrices and orthogonality relations
Formal duality, the distribution vector of a subset
Delsarte's inequalities
Polynomial schemes
Perfect codes and tight designs
Algebraic graph theory: eigenvalue techniques / 31.:
Tournaments and the Graham-Pollak theorem
The spectrum of a graph
Hoffman's theorem
Shannon capacity
Applications of interlacing and Perron-Frobenius
Graphs: planarity and duality / 32.:
Deletion and contraction
The chromatic polynomial, Euler's formula
Whitney duality, matroids
Graphs: colorings and embeddings / 33.:
The Five Color Theorem, embeddings and colorings on arbitrary surfaces
The Heawood conjecture
The Edmonds embedding technique
Electrical networks and squared squares / 34.:
The matrix-tree theorem
The network of a squared rectangle
Kirchhoff's theorem
Polya theory of counting / 35.:
The cycle index of a permutation group
Counting orbits
Weights, necklaces, the symmetric group
Stirling numbers
Baranyai's theorem / 36.:
One-factorizations of complete graphs and complete designs
Hints and comments on problems / Appendix 1.:
Hints
Suggestions
Comments on the problems in each chapter
Formal power series / Appendix 2.:
Formal power series ring, formal derivatives
Inverse functions
Residues
The Lagrange-Burmann formula
Name Index
Subject Index
Preface to the first edition
Preface to the second edition
Search trees
Strong connectivity
The Lovasz sieve
A generalization of Birkhoff's theorem
Circulations
Two (0, 1 *) problems: addressing for graphs and a hash-coding scheme
Associative block designs
The function P[subscript k] (n)
(0, 1)-Matrices
Counting (0, 1)-matrices
Partial and incomplete Latin squares
The Dinitz conjecture
Hadamard matrices, Reed--Muller codes
Counting
(higher) incidence matrices
The Wilson--Petrenjuk theorem
The Bruck--Ryser--Chowla theorem
The Assmus--Mattson theorem
The Bose--Mesner algebra
Directed strongly regular graphs
Neighborhood regular graphs
The Bose--Parker--Shrikhande theorem
Difference methods
Orthogonal subsquares
Duality
Chains in the lattice of subspaces
q-analogue of Sperner's theorem
The Mobius function
Chromatic polynomial of a graph
MDS codes
Block's lemma
Paley--Todd and Stanton--Sprott difference sets
The eigenmatrices and orthogonality relations
Formal duality
The distribution vector of a subset
(More) algebraic techniques in graph theory
Tournaments and the Graham--Pollak theorem
Applications of interlacing and Perron--Frobenius
Graph connectivity
Vertex connectivity
Menger's theorem
Tutte connectivity
Planarity and coloring
The chromatic polynomial
Kuratowski's theorem
Euler's formula
The Five Color Theorem
List-colorings
Whitney Duality
Whitney duality
Circuits and cutsets
MacLane's theorem
Embeddings of graphs on surfaces
Embeddings on arbitrary surfaces
The Ringel--Youngs theorem
Weights / 37.:
Necklaces
The symmetric group
Formal power series ring / 38.:
Formal derivatives
The Lagrange--Burmann formula
Preface
Graphs / 1.:
Terminology of graphs and digraphs
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