Combinatorial Enumeration

ISBN-10: 0486435970

ISBN-13: 9780486435978

Edition: 2004

Authors: Ian P. Goulden, David M. Jackson

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Description:

This graduate-level text presents an encyclopedic account of the mathematical theory and problem-solving techniques associated with enumeration problems. Its approach blends combinatorial and algebraic ideas to offer insights into a wide variety of problems, and each section of the book focuses on a specific discrete structure, advancing from elementary (often classical) results to those at research level. Subjects include the combinatorics of the ordinary generating function and the exponential generating function, the combinatorics of sequences, and the combinatorics of paths. The text is complemented by approximately 350 exercises with full solutions. 1983 ed. Foreword by Gian-Carlo Rota. References. Index.
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Book details

List price: $34.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 6/23/2004
Binding: Paperback
Pages: 608
Size: 5.25" wide x 8.25" long x 1.25" tall
Weight: 1.386
Language: English

Notation
Mathematical Preliminaries
The Ring of Formal Power Series
The Lagrange Theorem for Implicit Functions
The Combinatorics of the Ordinary Generating Function
Introduction
The Elementary Counting Lemmas
Preliminary Examples
Sequences
Partitions of an Integer
Inversions in Permutations and q-Identities
Planted Plane Trees
Sequences with Distinguished Substrings
Rooted Planar Maps and the Quadratic Method
The Combinatorics of the Exponential Generating Function
Introduction
The Elementary Counting Lemmas
Trees and Cycles in Permutations and Functions
2-Covers of a Set and Homeomorphically Irreducible Labeled Graphs
Coefficient Extraction for Symmetric Functions
The Combinatorics of Sequences
Introduction
The Maximal String Decomposition Theorem
The Pattern Algebra
The Logarithmic Connection for Circular Permutations
Permanents and Absolute Problems
The Combinatorics of Paths
Introduction
Weighted Paths
Lattice Paths
Ordered Sets of Paths
A q-Analogue of the Lagrange Theorem
Solutions
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
References
Index
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