Combinatorics

__NOTOC__ __NOEDITSECTION__ This preliminary outline is at present incomplete Your 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 The Pigeon Hole 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. Sequences and Partial Orders Ramsey Theory Ramsey's Theorem Bounds for Ramsey numbers Schur's Theorem Discrete mathematics University level mathematics books C 25%