Introductory combinatorics (Book, 2010) [WorldCat.org]
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Introductory combinatorics

Author: Richard A Brualdi
Publisher: Upper Saddle River, N.J. : Pearson/Prentice Hall, 2010
Edition/Format:   Print book : English : 5. updated editionView all editions and formats
Summary:

Appropriate for an undergraduate mathematics course on combinatorics. It emphasizes combinatorial ideas including the pigeon-hole principle, counting techniques, permutations and combinations, Polya  Read more...

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Genre/Form: Textbooks
Document Type: Book
All Authors / Contributors: Richard A Brualdi
ISBN: 0131001191 9780131001190 9780136020400 0136020402
OCLC Number: 488356839
Description: xii, 605 p. : illustrations ; 24 cm
Contents: 1. What is Combinatorics?1.1 Example: Perfect Covers of Chessboards1.2 Example: Magic Squares1.3 Example: The Four-Color Problem1.4 Example: The Problem of the 36 Officers1.5 Example: Shortest-Route Problem1.6 Example: Mutually Overlapping Circles1.7 Example: The Game of Nim 2. The Pigeonhole Principle2.1 Pigeonhole Principle: Simple Form2.2 Pigeonhole Principle: Strong Form2.3 A Theorem of Ramsay 3. Permutations and Combinations3.1 Four Basic Counting Principles3.2 Permutations of Sets3.3 Combinations of Sets3.4 Permutations of Multisets3.5 Combinations of Multisets3.6 Finite Probability 4. Generating Permutations and Combinations4.1 Generating Permutations4.2 Inversions in Permutations4.3 Generating Combinations4.4 Generating r-Combinations4.5 Partial Orders and Equivalence Relations 5. The Binomial Coefficients5.1 Pascal's Formula5.2 The Binomial Theorem5.3 Unimodality of Binomial Coefficients5.4 The Multinomial Theorem5.5 Newton's Binomial Theorem5.6 More on Partially Ordered Sets 6. The Inclusion-Exclusion Principle and Applications6.1 The Inclusion-Exclusion Principle6.2 Combinations with Repetition6.3 Derangements6.4 Permutations with Forbidden Positions6.5 Another Forbidden Position Problem6.6 Moebius Inversion 7. Recurrence Relations and Generating Functions7.1 Some Number Sequences7.2 Generating Functions7.3 Exponential Generating Functions7.4 Solving Linear Homogeneous Recurrence Relations7.5 Nonhomogeneous Recurrence Relations7.6 A Geometry Example 8. Special Counting Sequences8.1 Catalan Numbers8.2 Difference Sequences and Stirling Numbers8.3 Partition Numbers8.4 A Geometric Problem8.5 Lattice Paths and Schroeder Numbers 9. Systems of Distinct Representatives9.1 General Problem Formulation9.2 Existence of SDRs9.3 Stable Marriages 10. Combinatorial Designs10.1 Modular Arithmetic10.2 Block Designs10.3 Steiner Triple Systems10.4 Latin Squares 11. Introduction to Graph Theory11.1 Basic Properties11.2 Eulerian Trails11.3 Hamilton Paths and Cycles11.4 Bipartite Multigraphs11.5 Trees11.6 The Shannon Switching Game11.7 More on Trees 12. More on Graph Theory12.1 Chromatic Number12.2 Plane and Planar Graphs12.3 A 5-color Theorem12.4 Independence Number and Clique Number12.5 Matching Number12.6 Connectivity 13. Digraphs and Networks13.1 Digraphs13.2 Networks13.3 Matching in Bipartite Graphs Revisited 14. Polya Counting14.1 Permutation and Symmetry Groups14.2 Burnside's Theorem14.3 Polya's Counting formula
Responsibility: Richard A. Brualdi

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