Combinatroics

Unit I: The sum rule and product rule, permutations and combinations, the Pigeonhole principle,
Ramsay numbers, Catalan numbers, sterling numbers. 15 Lectures
Unit II: Further basic tools, generalized permutations and combinations sequences and
selections, the inclusion and exclusion principle, systems of distinct representatives, solved
problems derangements and other constrain derangements. 15 Lectures
Unit III: Combinatorial number theory, the permanent of a matrix, Rook polynomials and Hit
polynomials, SDR and coverings, (Sperners theorem and Symmetric chain decomposition,
posets and Dilworth's theorem) statements. 15 Lectures
Unit IV: Generating functions and recurrence relations, ordinary and exponential generating
functions, partitions of a positive integer, recurrence relations, algebraic solutions of linear
recurrence relations with constant coefficients and solutions of recurrence relations using
generating functions. 15 Lectures