9780136020400

Introductory Combinatorics

by
  • ISBN13:

    9780136020400

  • ISBN10:

    0136020402

  • Edition: 5th
  • Format: Hardcover
  • Copyright: 12/28/2008
  • Publisher: Pearson

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Summary

This trusted best-seller emphasizes combinatorial ideasincluding the pigeon-hole principle, counting techniques, permutations and combinations, Poacute;lya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, combinatortial structures (matchings, designs, graphs), and flows in networks. The Fifth Edition clarifies the exposition throughout and adds a wealth of new exercises.Appropriate for one- or two-semester, junior- to senior-level combinatorics courses.

Author Biography

Richard A. Brualdi is Bascom Professor of Mathematics, Emeritus at the University of Wisconsin-Madison. He served as Chair of the Department of Mathematics from 1993-1999. His research interests lie in matrix theory and combinatorics/graph theory. Professor Brualdi is the author or co-author of six books, and has published extensively. He is one of the editors-in-chief of the journal "Linear Algebra and its Applications" and of the journal "Electronic Journal of Combinatorics." He is a member of the American Mathematical Society, the Mathematical Association of America, the International Linear Algebra Society, and the Institute for Combinatorics and its Applications. He is also a Fellow of the Society for Industrial and Applied Mathematics.

Table of Contents

What is Combinatorics?
Example: Perfect Covers of Chessboards
Example: Magic Squares
Example: The Four-Color Problem
Example: The Problem of the 36 Officers
Example: Shortest-Route Problem
Example: Mutually Overlapping Circles
Example: The Game of Nim
The Pigeonhole Principle
Pigeonhole Principle: Simple Form
Pigeonhole Principle: Strong Form
A Theorem of Ramsay
Permutations and Combinations
Four Basic Counting Principles
Permutations of Sets
Combinations of Sets
Permutations of Multisets
Combinations of Multisets
Finite Probability
Generating Permutations and Combinations
Generating Permutations
Inversions in Permutations
Generating Combinations
Generating r-Combinations
Partial Orders and Equivalence Relations
The Binomial Coefficients
Pascal's Formula
The Binomial Theorem
Unimodality of Binomial Coefficients
The Multinomial Theorem
Newton's Binomial Theorem
More on Partially Ordered Sets
The Inclusion-Exclusion Principle and Applications
The Inclusion-Exclusion Principle
Combinations with Repetition
Derangements
Permutations with Forbidden Positions
Another Forbidden Position Problem
Möbius Inversion
Recurrence Relations and Generating Functions
Some Number Sequences
Generating Functions
Exponential Generating Functions
Solving Linear Homogeneous Recurrence Relations
Nonhomogeneous Recurrence Relations
A Geometry Example
Special Counting Sequences
Catalan Numbers
Difference Sequences and Stirling Numbers
Partition Numbers
A Geometric Problem
Lattice Paths and Schröder Numbers
Systems of Distinct Representatives
General Problem Formulation
Existence of SDRs
Stable Marriages
Combinatorial Designs
Modular Arithmetic
Block Designs
Steiner Triple Systems
Latin Squares
Introduction to Graph Theory
Basic Properties
Eulerian Trails
Hamilton Paths and Cycles
Bipartite Multigraphs
Trees
The Shannon Switching Game
More on Trees
More on Graph Theory
Chromatic Number
Plane and Planar Graphs
A 5-color Theorem
Independence Number and Clique Number
Matching Number
Connectivity
Digraphs and Networks
Digraphs
Networks
Matching in Bipartite Graphs Revisited
Pólya Counting
Permutation and Symmetry Groups
Burnside's Theorem
Pólya's Counting formula
Table of Contents provided by Publisher. All Rights Reserved.

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