A course in combinatorics

Başlık:

Yazar:

Lint, Jacobus Hendricus van, 1932-2004.

ISBN:

9780521006019

Ek Yazar:

Lint, Jacobus Hendricus van, 1932-2004.

Edition:

Third ed.

Fiziksel Tanım:

XIV, 602 sayfa ; 26 sm.

General Note:

Bibliyografya ve indeks.

Contents:

1. Graphs 1 --

Konu Terimleri:

Combinatorial analysis

Kombinatoryal analiz

Mevcut:*

Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	Kitap	0133205	QA164 .L56 2002	Searching... Unknown

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

Preface to the first edition	p. xi
Preface to the second edition	p. xiii
1. Graphs	p. 1
Terminology of graphs and digraphs
Eulerian circuits
Hamiltonian circuits
2. Trees	p. 12
Cayley's theorem
Spanning trees and the greedy algorithm
Search trees
Strong connectivity
3. Colorings of graphs and Ramsey's theorem	p. 24
Brooks' theorem
Ramsey's theorem and Ramsey numbers
The Lovasz sieve
The Erdos-Szekeres theorem
4. Turan's theorem and extremal graphs	p. 37
Turan's theorem and extremal graph theory
5. Systems of distinct representatives	p. 43
Bipartite graphs
P. Hall's condition
SDRs
Konig's theorem
Birkhoff's theorem
6. Dilworth's theorem and extremal set theory	p. 53
Partially ordered sets
Dilworth's theorem
Sperner's theorem
Symmetric chains
The Erdos-Ko-Rado theorem
7. Flows in networks	p. 61
The Ford-Fulkerson theorem
The integrality theorem
A generalization of Birkhoff's theorem
Circulations
8. De Bruijn sequences	p. 71
The number of De Bruijn sequences
9. Two (0, 1 *) problems: addressing for graphs and a hash-coding scheme	p. 77
Quadratic forms
Winkler's theorem
Associative block designs
10. The principle of inclusion and exclusion; inversion formulae	p. 89
Inclusion-exclusion
Derangements
Euler indicator
Mobius function
Mobius inversion
Burnside's lemma
Probleme des menages
11. Permanents	p. 98
Bounds on permanents
Schrijver's proof of the Minc conjecture
Fekete's lemma
Permanents of doubly stochastic matrices
12. The Van der Waerden conjecture	p. 110
The early results of Marcus and Newman
London's theorem
Egoritsjev's proof
13. Elementary counting; Stirling numbers	p. 119
Stirling numbers of the first and second kind
Bell numbers
Generating functions
14. Recursions and generating functions	p. 129
Elementary recurrences
Catalan numbers
Counting of trees
Joyal theory
Lagrange inversion
15. Partitions	p. 152
The function P[subscript k] (n)
The partition function
Ferrers diagrams
Euler's identity
Asymptotics
The Jacobi triple product identity
Young tableaux and the hook formula
16. (0, 1)-Matrices	p. 169
Matrices with given line sums
Counting (0, 1)-matrices
17. Latin squares	p. 182
Orthogonal arrays
Conjugates and isomorphism
Partial and incomplete Latin squares
Counting Latin squares
The Evans conjecture
The Dinitz conjecture
18. Hadamard matrices, Reed--Muller codes	p. 199
Hadamard matrices and conference matrices
Recursive constructions
Paley matrices
Williamson's method
Excess of a Hadamard matrix
First order Reed-Muller codes
19. Designs	p. 215
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
20. Codes and designs	p. 244
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
21. Strongly regular graphs and partial geometries	p. 261
The Bose--Mesner algebra
Eigenvalues
The integrality condition
Quasisymmetric designs
The Krein condition
The absolute bound
Uniqueness theorems
Partial geometries
Examples
Directed strongly regular graphs
Neighborhood regular graphs
22. Orthogonal Latin squares	p. 283
Pairwise orthogonal Latin squares and nets
Euler's conjecture
The Bose--Parker--Shrikhande theorem
Asymptotic existence
Orthogonal arrays and transversal designs
Difference methods
Orthogonal subsquares
23. Projective and combinatorial geometries	p. 303
Projective and affine geometries
Duality
Pasch's axiom
Desargues' theorem
Combinatorial geometries
Geometric lattices
Greene's theorem
24. Gaussian numbers and q-analogues	p. 325
Chains in the lattice of subspaces
q-analogue of Sperner's theorem
Interpretation of the coefficients of the Gaussian polynomials
Spreads
25. Lattices and Mobius inversion	p. 333
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
MDS codes
26. Combinatorial designs and projective geometries	p. 351
Arcs and subplanes in projective planes
Blocking sets
Quadratic and Hermitian forms
Unitals
Generalized quadrangles
Mobius planes
27. Difference sets and automorphisms	p. 369
Block's lemma
Automorphisms of symmetric designs
Paley--Todd and Stanton--Sprott difference sets
Singer's theorem
28. Difference sets and the group ring	p. 383
The Multiplier Theorem and extensions
Homomorphisms and further necessary conditions
29. Codes and symmetric designs	p. 396
The sequence of codes of a symmetric design
Wilbrink's theorem
30. Association schemes	p. 405
Examples
The eigenmatrices and orthogonality relations
Formal duality
The distribution vector of a subset
Delsarte's inequalities
Polynomial schemes
Perfect codes and tight designs
31. (More) algebraic techniques in graph theory	p. 432
Tournaments and the Graham--Pollak theorem
The spectrum of a graph
Hoffman's theorem
Shannon capacity
Applications of interlacing and Perron--Frobenius
32. Graph connectivity	p. 451
Vertex connectivity
Menger's theorem
Tutte connectivity
33. Planarity and coloring	p. 459
The chromatic polynomial
Kuratowski's theorem
Euler's formula
The Five Color Theorem
List-colorings
34. Whitney Duality	p. 472
Whitney duality
Circuits and cutsets
MacLane's theorem
35. Embeddings of graphs on surfaces	p. 491
Embeddings on arbitrary surfaces
The Ringel--Youngs theorem
The Heawood conjecture
The Edmonds embedding technique
36. Electrical networks and squared squares	p. 507
The matrix-tree theorem
De Bruijn sequences
The network of a squared rectangle
Kirchhoff's theorem
37. Polya theory of counting	p. 522
The cycle index of a permutation group
Counting orbits
Weights
Necklaces
The symmetric group
Stirling numbers
38. Baranyai's theorem	p. 536
One-factorizations of complete graphs and complete designs
Appendix 1. Hints and comments on problems	p. 542
Hints
Suggestions
Comments on the problems in each chapter
Appendix 2. Formal power series	p. 578
Formal power series ring
Formal derivatives
Inverse functions
Residues
The Lagrange--Burmann formula
Name Index	p. 584
Subject Index	p. 590

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