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