Combinatorics

Lecture 1 - Pigeon hole principle - (Part 1)

Lecture 2 - Pigeon hole principle - (Part 2)

Lecture 3 - Pigeon hole principle - (Part 3)

Lecture 4 - Pigeon hole principle - (Part 4)

Lecture 5 - Elementary concepts and basic counting principles

Lecture 6 - Elementary concepts; Binomial theorem; Bijective proofs - Part (1)

Lecture 7 - Bijective proofs – Part (2)

Lecture 8 - Bijective proofs - Part (3); Properties of binomial coefficients; Combinatorial identities - Part (1)

Lecture 9 - Combinatorial identities - Part (2); Permutations of multisets – Part (1)

Lecture 10 - Permutations of multisets – Part (2)

Lecture 11 - Multinomial Theorem, Combinations of Multisets – Part (1)

Lecture 12 - Combinations of Multisets - Part (2)

Lecture 13 - Combinations of Multisets – Part (3), Bounds for binomial coefficients

Lecture 14 - Sterling’s Formula, Generalization of Binomial coefficients - Part (1)

Lecture 15 - Generalization of Binomial coefficients - Part (2)

Lecture 16 - Generalization of Binomial coefficients - Part (3); Double counting - Part (1)

Lecture 17 - Double counting - Part (2)

Lecture 18 - Hall’s Theorem for regular bipartite graphs; Inclusion exclusion principle - Part (1)

Lecture 19 - Inclusion exclusion principle - Part (2)

Lecture 20 - Inclusion exclusion principle - Part (3)

Lecture 21 - Inclusion exclusion principle - Part (4)

Lecture 22 - Inclusion exclusion principle - Part (5)

Lecture 23 - Recurrence Relations - Part (1)

Lecture 24 - Recurrence Relations - Part (2)

Lecture 25 - Recurrence Relations - Part (3)

Lecture 26 - Recurrence Relations - Part (4)

Lecture 27 - Recurrence Relations - Part (5)

Lecture 28 - Generating functions - Part (1)

Lecture 29 - Generating functions - Part (2)

Lecture 30 - Solving recurrence relations using generating functions - Part (1)

Lecture 31 - Solving recurrence relations using generating functions - Part (2)

Lecture 32 - Exponential generating functions - Part (1)

Lecture 33 - Exponential generating functions - Part (2), Partition Number - Part (1)

Lecture 34 - Partition Number - Part (2)

Lecture 35 - Partition Number - Part (3)

Lecture 36 - Partition Number - Part (4); Catalan Numbers - Part (1)

Lecture 37 - Catalans Numbers - Part (2)

Lecture 38 - Catalan Numbers - Part (3), Sterling numbers of the 2nd kind

Lecture 39 - Difference Sequences

Lecture 40 - Sterling Numbers

Lecture 41 - Summary