Combinatorics

Preliminaries

The Pigeonhole Principle

Pairing problem

  • General principles
  • P. Hall's selection theorem
  • Applications to Latin squares and to coverings by dominoes of pruned chessboards.

The inclusion-exclusion principal

  • Applications to derangements
  • Applications to counting problems
  • Applications to rook polynomialss

Linear recurrence relations

Generating functions

Catalan numbers

Partitions

  • Counting various types of partitions
  • Ferrers graphs
  • Self-conjugate partitions

Symmetric functions (and anti-symmetric functions)

  • Monomial symmetric functions
  • Elementary symmetric functions
  • Theory of equations
  • Newton's formulae and relations between symmetric functions
  • Indexing of symmetric functions by partitions.

Sequences and Partial Orders

Ramsey Theory

Last modified on 22 September 2010, at 17:22