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A course in combinatorics / J.H. van Lint and R.M. Wilson.
Math/Physics/Astronomy Library QA164 .L56 2001
Available
- Format:
- Book
- Author/Creator:
- Lint, Jacobus Hendricus van, 1932-
- Language:
- English
- Subjects (All):
- Combinatorial analysis.
- Physical Description:
- xiv, 602 pages : illustrations ; 26 cm
- Edition:
- Second edition.
- Place of Publication:
- Cambridge, U.K. ; New York : Cambridge University Press, 2001.
- Summary:
- Second edition of a popular text which covers the whole field of combinatorics.
- Contents:
- 1. Graphs 1
- Terminology of graphs and digraphs
- Eulerian circuits
- Hamiltonian circuits
- 2. Trees 12
- Cayley's theorem
- Spanning trees and the greedy algorithm
- Search trees
- Strong connectivity
- 3. Colorings of graphs and Ramsey's theorem 24
- Brooks' theorem
- Ramsey's theorem and Ramsey numbers
- The Lovasz sieve
- The Erdos-Szekeres theorem
- 4. Turan's theorem and extremal graphs 37
- Turan's theorem and extremal graph theory
- 5. Systems of distinct representatives 43
- Bipartite graphs
- P. Hall's condition
- SDRs
- Konig's theorem
- Birkhoff's theorem
- 6. Dilworth's theorem and extremal set theory 53
- Partially ordered sets
- Dilworth's theorem
- Sperner's theorem
- Symmetric chains
- The Erdos-Ko-Rado theorem
- 7. Flows in networks 61
- The Ford-Fulkerson theorem
- The integrality theorem
- A generalization of Birkhoff's theorem
- Circulations
- 8. De Bruijn sequences 71
- The number of De Bruijn sequences
- 9. Two (0, 1 *) problems: addressing for graphs and a hash-coding scheme 77
- Quadratic forms
- Winkler's theorem
- Associative block designs
- 10. The principle of inclusion and exclusion; inversion formulae 89
- Inclusion-exclusion
- Derangements
- Euler indicator
- Mobius function
- Mobius inversion
- Burnside's lemma
- Probleme des menages
- 11. Permanents 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 110
- The early results of Marcus and Newman
- London's theorem
- Egoritsjev's proof
- 13. Elementary counting; Stirling numbers 119
- Stirling numbers of the first and second kind
- Bell numbers
- Generating functions
- 14. Recursions and generating functions 129
- Elementary recurrences
- Catalan numbers
- Counting of trees
- Joyal theory
- Lagrange inversion
- 15. Partitions 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 169
- Matrices with given line sums
- Counting (0, 1)-matrices
- 17. Latin squares 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 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 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 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 261
- The Bose
- Mesner algebra
- Eigenvalues
- The integrality condition
- Quasisymmetric designs
- The Krein condition
- The absolute bound
- Uniqueness theorems
- Partial geometries
- Directed strongly regular graphs
- Neighborhood regular graphs
- 22. Orthogonal Latin squares 283
- Pairwise orthogonal Latin squares and nets
- Euler's conjecture
- Parker
- Shrikhande theorem
- Asymptotic existence
- Orthogonal arrays and transversal designs
- Difference methods
- Orthogonal subsquares
- 23. Projective and combinatorial geometries 303
- Projective and affine geometries
- Duality
- Pasch's axiom
- Desargues' theorem
- Combinatorial geometries
- Geometric lattices
- Greene's theorem
- 24. Gaussian numbers and q-analogues 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 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 351
- Arcs and subplanes in projective planes
- Blocking sets
- Quadratic and Hermitian forms
- Unitals
- Generalized quadrangles
- Mobius planes
- 27. Difference sets and automorphisms 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 383
- The Multiplier Theorem and extensions
- Homomorphisms and further necessary conditions
- 29. Codes and symmetric designs 396
- The sequence of codes of a symmetric design
- Wilbrink's theorem
- 30. Association schemes 405
- 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 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 451
- Vertex connectivity
- Menger's theorem
- Tutte connectivity
- 33. Planarity and coloring 459
- The chromatic polynomial
- Kuratowski's theorem
- Euler's formula
- The Five Color Theorem
- List-colorings
- 34. Whitney Duality 472
- Whitney duality
- Circuits and cutsets
- MacLane's theorem
- 35. Embeddings of graphs on surfaces 491
- Embeddings on arbitrary surfaces
- The Ringel
- Youngs theorem
- The Heawood conjecture
- The Edmonds embedding technique
- 36. Electrical networks and squared squares 507
- The matrix-tree theorem
- De Bruijn sequences
- The network of a squared rectangle
- Kirchhoff's theorem
- 37. Polya theory of counting 522
- The cycle index of a permutation group
- Counting orbits
- Weights
- Necklaces
- The symmetric group
- Stirling numbers
- 38. Baranyai's theorem 536
- One-factorizations of complete graphs and complete designs
- Appendix 1. Hints and comments on problems 542
- Hints
- Suggestions
- Comments on the problems in each chapter
- Appendix 2. Formal power series 578
- Formal power series ring
- Formal derivatives
- Inverse functions
- Residues
- The Lagrange
- Burmann formula.
- Notes:
- Includes bibliographical references and indexes.
- ISBN:
- 0521803403
- 0521006015
- OCLC:
- 48531921
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