# Combinatorics

This preliminary outline is at present incompleteYour suggestions in improving it are welcome. Please either edit this page to include your suggestions or leave them at the book's discussion page. |

## Preliminaries

- What is Combinatorics?
- Motivating Examples and Problems
- Counting
- Subsets of a set-The Binomial Coefficient
- Binomial Theorem
- Congruences

## 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 polynomials

## 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.