A course in combinatorics

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A course in combinatorics / J.H. van Lint and R.M. Wilson

資料種別:

図書

出版情報:

Cambridge ; New York : Cambridge University Press, c1992

形態:

xii, 530 p. ; 26 cm

著者名:

ISBN:

9780521410571 [0521410576] (: hbk)
9780521422604 [0521422604] (: pbk)

書誌ID:

BA18979570

子書誌情報

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他の版・巻

A course in combinatorics. 2nd ed (: hard ; : pbk)
J.H. van Lint and R.M. Wilson , Cambridge University Press , 2001

書誌詳細

注記:

Includes bibliographical references and indexes

主題:

順列と組合せ

言語:

英語

目次情報:

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

Eulerian circuits

Hamiltonian circuits

Trees / 2.：

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