Applied Combinatorics, 5th Edition,9780471735076

Applied Combinatorics, 5th Edition

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Edition: 5th
ISBN13: 9780471735076
ISBN10: 0471735078
Format: Hardcover
Pub. Date: 2006-11-01
Publisher(s): WILEY
List Price: $205.90

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Summary

Updated with new material, this"Fifth Edition" of the most widely used book in combinatorial problems explains how to reason and model combinatorically. It also stresses the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Combinatorical reasoning underlies all analysis of computer systems. It plays a similar role in discrete operations research problems and in finite probability. This bookseeks to develop proficiency in basic discrete math problem solving in the way that a calculus text develops proficiency in basic analysis problem solving.

Author Biography

Alan Tucker is Deputy Department Chair and Undergraduate Program Director in the Department of Applied Mathematics and Statistics at SUNY Stony Brook.

Table of Contents

Prelude xi
PART ONE GRAPH THEORY
1(174)
Elements of Graph Theory
3(46)
Graph Models
3(10)
Isomorphism
13(10)
Edge Counting
23(6)
Planar Graphs
29(13)
Summary and References
42(7)
Supplementary Exercises
43(6)
Covering Circuits and Graph Coloring
49(44)
Euler Cycles
49(7)
Hamilton Circuits
56(12)
Graph Coloring
68(9)
Coloring Theorems
77(8)
Summary and References
85(8)
Supplement Graph Model for Instant Insanity
86(5)
Supplement Exercises
91(2)
Trees and Searching
93(34)
Properties of Trees
93(10)
Search Trees and Spanning Trees
103(10)
The Traveling Salesperson Problem
113(8)
Tree Analysis of Sorting Algorithms
121(4)
Summary and References
125(2)
Network Algorithms
127(48)
Shortest Paths
127(4)
Minimal Spanning Trees
131(4)
Network Flows
135(18)
Algorithmic Matching
153(10)
The Transportation Problem
163(11)
Summary and References
174(1)
PART TWO ENUMERATION
175(172)
General Counting Methods for Arrangements and Selections
177(68)
Two Basic Counting Principles
177(10)
Simple Arrangements and Selections
187(15)
Arrangements and Selections with Repetitions
202(8)
Distributions
210(13)
Binomial Identities
223(9)
Summary and References
232(13)
Supplement Selected Solutions to Problems in Chapter 5
233(12)
Generating Functions
245(34)
Generating Function Models
245(7)
Calculating Coefficients of Generating Functions
252(10)
Partitions
262(5)
Exponential Generating Functions
267(6)
A Summation Method
273(4)
Summary and References
277(2)
Recurrence Relations
279(36)
Recurrence Relation Models
279(12)
Divide-and-Conquer Relations
291(5)
Solution of Linear Recurrence Relations
296(4)
Solution of Inhomogeneous Recurrence Relations
300(4)
Solutions with Generating Functions
304(8)
Summary and References
312(3)
Inclusion--Exclusion
315(32)
Counting with Venn Diagrams
315(8)
Inclusion--Exclusion Formula
323(12)
Restricted Positions and Rook Polynomials
335(10)
Summary and Reference
345(2)
PART THREE ADDITIONAL TOPICS
347(64)
Polya's Enumeration Formula
349(28)
Equivalence and Symmetry Groups
349(8)
Burnside's Theorem
357(5)
The Cycle Index
362(7)
Polya's Formula
369(7)
Summary and References
376(1)
Computer Science Approaches to Enumeration
377(18)
Generating Permutations and Combinations and Programming Projects
377(6)
Formal Languages and Grammars
383(5)
Finite-State Machines
388(5)
Summary and References
393(2)
Games with Graphs
395(16)
Progressively Finite Games
395(8)
Nim-Type Games
403(7)
Summary and References
410(1)
APPENDIX
411(20)
Set Theory
411(5)
Mathematical Induction
416(3)
A Little Probability
419(4)
The Pigeonhole Principle
423(3)
Computational Complexity and NP-completeness
426(5)
Glossary of Counting and Graph Theory Terms 431(4)
Bibliography 435(2)
Solutions to Odd-Numbered Problems 437(34)
Index 471

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