Enumerative Combinatorics: Volume 1

ISBN-10: 1107602629
ISBN-13: 9781107602625
Edition: 2nd 2011
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Description: Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300  More...

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Book details

List price: $89.95
Edition: 2nd
Copyright year: 2011
Publisher: Cambridge University Press
Publication date: 12/12/2011
Binding: Paperback
Pages: 642
Size: 6.00" wide x 9.00" long x 1.25" tall
Weight: 2.222
Language: English

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.

Richard P. Stanley is a Professor of Applied Mathematics at the Massachusetts Institute of Technology. He is universally recognized as a leading expert in the field of combinatorics and its applications to a variety of other mathematical disciplines. He won the AMS 2001 Leroy P. Steele Prize for Mathematical Exposition for his books Enumerative Combinatorics, Volumes 1 and 2, which contain material that form the basis for much of the present book.

Preface
Acknowledgments
What Is Enumerative Combinatorics?
How to Count
Sets and Multisets
Cycles and Inversions
Descents
Geometric Representations of Permutations
Alternating Permutations, Euler Numbers, and the cd-lndex of $$$n
Permutations of Multisets
Partition Identities
The Twelvefold Way
Two q-Analogues of Permutations
Notes
Bibliography
Exercises for Chapter 1
Solutions to Exercises
Sieve Methods
Inclusion-Exclusion
Examples and Special Cases
Permutations with Restricted Position
Ferrers Boards
V-Partitions and Unimodal Sequences
Involutions
Determinants
Notes
Bibliography
Exercises for Chapter 2
Solutions to Exercises
Partially Ordered Sets
Basic Concepts
New Posets from Old
Lattices
Distributive Lattices
Chains in Distributive Lattices
Incidence Algebras
The M�bius Inversion Formula
Techniques for Computing M�bius Functions
Lattices and Their M�bius Functions
The Mobius Function of a Semimodular Lattice
Hyperplane Arrangements
Zeta Polynomials
Rank Selection
R-Labelings
(P,�)-Partitions
Eulerian Posets
The cd-Index of an Eulerian Poset
Binomial Posets and Generating Functions
An Application to Permutation Enumeration
Promotion and Evacuation
Differential Posets
Notes
Bibliography
Exercises for Chapter 3
Solutions to Exercises
Rational Generating Functions
Rational Power Series in One Variable
Further Ramifications
Polynomials
Quasipolynomials
Linear Homogeneous Diophantine Equations
Applications
The Transfer-Matrix Method
Notes
Bibliography
Exercises for Chapter 4
Solutions to Exercises
Appendix: Graph Theory Terminology
First Edition Numbering
List of Notation (Partial)
Index

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