Stanley R. Enumerative Combinatorics. Vol 1. 2ed 2011

Textbook in PDF format

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-index of Sn
Permutations of multisets
Partition identities
The Twelvefold Way
Two q-analogues of permutations
Notes
Exercises
Solutions to exercises
Sieve Methods
Inclusion-Exclusion
Examples and Special Cases
Permutations with Restricted Positions
Ferrers Boards
V -partitions and Unimodal Sequences
Involutions
Determinants
Notes
Exercises
Solutions to exercises
Partially Ordered Sets
Basic Concepts
New Posets from Old
Lattices
Distributive Lattices
Chains in Distributive Lattices
Incidence Algebras
The M¨obius Inversion Formula
Techniques for Computing M¨obius Functions
Lattices and Their M¨obius Functions
The M¨obius 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
Exercises
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
Exercises
Solutions to exercises
Appendix Graph Theory Terminology
First Edition Numbering
List of Notation