Combinatorics

Overview

Pigeon hole Principle - Elementary Concepts - Elementary concepts and basic counting principles - Elementary concepts; Binomial theorem; Bijective proofs - Properties of binomial coefficients; Combinatorial identities - Permutations of multisets - Multinomial Theorem, Combinations of Multisets - Bounds for binomial coefficients - Sterlings Formula, Generalization of Binomial coefficients - Double counting;Some Techniques:Double counting - Halls Theorem for regular bipartite graphs; Inclusion exclusion principle - Recurrence relations and generating functions:Recurrence Relations - Generating functions - Solving recurrence relations using generating functions - Exponential generating functions - Special numbers - Partition Number - Catalan Numbers - Difference Sequences - Sterling Numbers