Preface to the Second Edition
Updated Preface to the First Edition
Contents
Basic Notation
1 Walks in Graphs
Notes for Chapter 1
Exercises for Chapter 1
2 Cubes and the Radon Transform
Notes for Chapter 2
Exercises for Chapter 2
3 Random Walks
Notes for Chapter 3
Exercises for Chapter 3
4 The Sperner Property
Notes for Chapter 4
Exercises for Chapter 4
5 Group Actions on Boolean Algebras
Notes for Chapter 5
Exercises for Chapter 5
6 Young Diagrams and q-Binomial Coefficients
Notes for Chapter 6
Exercises for Chapter 6
7 Enumeration Under Group Action
Notes for Chapter 7
Exercises for Chapter 7
8 A Glimpse of Young Tableaux
Appendix 1: The RSK Algorithm
Appendix 2: Plane Partitions
Notes for Chapter 8
Exercises for Chapter 8
9 The Matrix-Tree Theorem
Appendix: Three Elegant Combinatorial Proofs
Notes for Chapter 9
Exercises for Chapter 9
10 Eulerian Digraphs and Oriented Trees
Notes for Chapter 10
Exercises for Chapter 10
11 Cycles, Bonds, and Electrical Networks
11.1 The Cycle Space and Bond Space
11.2 Bases for the Cycle Space and Bond Space
11.3 Electrical Networks
11.4 Planar Graphs (Sketch)
11.5 Squaring the Square
Notes for Chapter 11
Exercises for Chapter 11
12 A Glimpse of Combinatorial Commutative Algebra
12.1 Simplicial Complexes
12.2 The Face Ring
Notes for Chapter 12
Exercises for Chapter 12
13 Miscellaneous Gems of Algebraic Combinatorics
13.1 The 100 Prisoners
13.2 Oddtown
13.3 Complete Bipartite Partitions of Kn
13.4 The Nonuniform Fisher Inequality
13.5 Odd Neighborhood Covers
13.6 Circulant Hadamard Matrices
13.7 P-Recursive Functions
13.8 Affine Monoids
Notes for Chapter 13
Exercises for Chapter 13
Hints and Comments for Some Exercises
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Bibliography
Index