R. Brualdi, Introductory Combinatorics, Fourth Edition. Prentice Hall,
1999
Course Description
The course discusses basic topics in Enumerative Combinatorics. We discuss
such combinatorial objects as finite sets and multisets, various classes
of maps between them, partitions, and lattice paths. Enumerating these
objects involves fundamental sequences of numbers: binomial coefficients,
Stirling numbers of the first and second kind, Catalan numbers, Eulerian
numbers, etc. We also discuss basic methods of enumeration: basic counting
rules, ordinary and exponential generating functions, finite differences,
linear recursions, inclusion-exclusion principle, Polya's theory.