Course in Combinatorics

ISBN-10: 0521006015

ISBN-13: 9780521006019

Edition: 2nd 2001 (Revised)

List price: $84.99 Buy it from $52.86
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Description: 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.

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Book details

List price: $84.99
Edition: 2nd
Copyright year: 2001
Publisher: Cambridge University Press
Publication date: 11/22/2001
Binding: Paperback
Pages: 620
Size: 6.75" wide x 9.50" long x 1.25" tall
Weight: 2.640
Language: English

Preface to the first edition
Preface to the second edition
Terminology of graphs and digraphs
Eulerian circuits
Hamiltonian circuits
Cayley's theorem
Spanning trees and the greedy algorithm
Search trees
Strong connectivity
Colorings of graphs and Ramsey's theorem
Brooks' theorem
Ramsey's theorem and Ramsey numbers
The Lovasz sieve
The Erdos-Szekeres theorem
Turan's theorem and extremal graphs
Turan's theorem and extremal graph theory
Systems of distinct representatives
Bipartite graphs
P. Hall's condition
Konig's theorem
Birkhoff's theorem
Dilworth's theorem and extremal set theory
Partially ordered sets
Dilworth's theorem
Sperner's theorem
Symmetric chains
The Erdos-Ko-Rado theorem
Flows in networks
The Ford-Fulkerson theorem
The integrality theorem
A generalization of Birkhoff's theorem
De Bruijn sequences
The number of De Bruijn sequences
Two (0, 1 *) problems: addressing for graphs and a hash-coding scheme
Quadratic forms
Winkler's theorem
Associative block designs
The principle of inclusion and exclusion; inversion formulae
Euler indicator
Mobius function
Mobius inversion
Burnside's lemma
Probleme des menages
Bounds on permanents
Schrijver's proof of the Minc conjecture
Fekete's lemma
Permanents of doubly stochastic matrices
The Van der Waerden conjecture
The early results of Marcus and Newman
London's theorem
Egoritsjev's proof
Elementary counting; Stirling numbers
Stirling numbers of the first and second kind
Bell numbers
Generating functions
Recursions and generating functions
Elementary recurrences
Catalan numbers
Counting of trees
Joyal theory
Lagrange inversion
The function P[subscript k] (n)
The partition function
Ferrers diagrams
Euler's identity
The Jacobi triple product identity
Young tableaux and the hook formula
(0, 1)-Matrices
Matrices with given line sums
Counting (0, 1)-matrices
Latin squares
Orthogonal arrays
Conjugates and isomorphism
Partial and incomplete Latin squares
Counting Latin squares
The Evans conjecture
The Dinitz conjecture
Hadamard matrices, Reed--Muller codes
Hadamard matrices and conference matrices
Recursive constructions
Paley matrices
Williamson's method
Excess of a Hadamard matrix
First order Reed-Muller codes
The Erdos-De Bruijn theorem
Steiner systems
Balanced incomplete block designs
Hadamard designs
(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
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
The Bose--Mesner algebra
The integrality condition
Quasisymmetric designs
The Krein condition
The absolute bound
Uniqueness theorems
Partial geometries
Directed strongly regular graphs
Neighborhood regular graphs
Orthogonal Latin squares
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
Projective and combinatorial geometries
Projective and affine geometries
Pasch's axiom
Desargues' theorem
Combinatorial geometries
Geometric lattices
Greene's theorem
Gaussian numbers and q-analogues
Chains in the lattice of subspaces
q-analogue of Sperner's theorem
Interpretation of the coefficients of the Gaussian polynomials
Lattices and Mobius inversion
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
Combinatorial designs and projective geometries
Arcs and subplanes in projective planes
Blocking sets
Quadratic and Hermitian forms
Generalized quadrangles
Mobius planes
Difference sets and automorphisms
Block's lemma
Automorphisms of symmetric designs
Paley--Todd and Stanton--Sprott difference sets
Singer's theorem
Difference sets and the group ring
The Multiplier Theorem and extensions
Homomorphisms and further necessary conditions
Codes and symmetric designs
The sequence of codes of a symmetric design
Wilbrink's theorem
Association schemes
The eigenmatrices and orthogonality relations
Formal duality
The distribution vector of a subset
Delsarte's inequalities
Polynomial schemes
Perfect codes and tight designs
(More) algebraic techniques in graph theory
Tournaments and the Graham--Pollak theorem
The spectrum of a graph
Hoffman's theorem
Shannon capacity
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
Whitney Duality
Whitney duality
Circuits and cutsets
MacLane's theorem
Embeddings of graphs on surfaces
Embeddings on arbitrary surfaces
The Ringel--Youngs theorem
The Heawood conjecture
The Edmonds embedding technique
Electrical networks and squared squares
The matrix-tree theorem
De Bruijn sequences
The network of a squared rectangle
Kirchhoff's theorem
Polya theory of counting
The cycle index of a permutation group
Counting orbits
The symmetric group
Stirling numbers
Baranyai's theorem
One-factorizations of complete graphs and complete designs
Hints and comments on problems
Comments on the problems in each chapter
Formal power series
Formal power series ring
Formal derivatives
Inverse functions
The Lagrange--Burmann formula
Name Index
Subject Index
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