# Combinatorics

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3 STUDENTS

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 – Sterling’s Formula, Generalization of Binomial coefficients – Double counting;Some Techniques:Double counting – Hall’s 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

### Course Curriculum

 Pigeon hole principle – (Part 1) Details 58:16 Pigeon hole principle – (Part 2) Details 58:4 Pigeon hole principle – (Part 3) Details 59:23 Pigeon hole principle – (Part 4) Details 59:10 Elementary concepts and basic counting principles Details 57:36 Elementary concepts; Binomial theorem; Bijective proofs – Part (1) Details 59:1 Bijective proofs — Part (2) Details 58:17 Bijective proofs – Part (3); Properties of binomial coefficients; Details 59:22 Combinatorial identities – Part (2); Permutations of multisets — Part (1) Details 59:10 Permutations of multisets — Part (2) Details 59:4 Multinomial Theorem, Combinations of Multisets — Part (1) Details 57:13 Combinations of Multisets – Part (2) Details 56:37 Combinations of Multisets — Part (3), Bounds for binomial coefficients Details 1:1:6 Sterling’s Formula, Generalization of Binomial coefficients – Part (1) Details 58:27 Generalization of Binomial coefficients – Part (2) Details 57:46 Generalization of Binomial coefficients – Part (3); Double counting – Part (1) Details 59:24 Double counting – Part (2) Details 58:40 Hall’s Theorem for regular bipartite graphs; Inclusion exclusion principle – Part (1) Details 59:21 Inclusion exclusion principle – Part (2) Details 59:23 Inclusion exclusion principle – Part (3) Details 57:34 Inclusion exclusion principle – Part (4) Details 59:24 Inclusion exclusion principle – Part (5) Details 58:37 Recurrence Relations – Part (1) Details 58:19 Recurrence Relations – Part (2) Details 56:12 Recurrence Relations – Part (3) Details 58:29 Recurrence Relations – Part (4) Details 58:29 Recurrence Relations – Part (5) Details 58:50 Generating functions – Part (1) Details 59:11 Generating functions – Part (2) Details 59:24 Solving recurrence relations using generating functions – Part (1) Details 59:12 Solving recurrence relations using generating functions – Part (2) Details 59:59 Exponential generating functions – Part (1) Details 59:4 Exponential generating functions – Part (2), Partition Number – Part (1) Details 57:18 Partition Number – Part (2) Details 58:30 Partition Number – Part (3) Details 56:52 Partition Number – Part (4); Catalan Numbers – Part (1) Details 58:3 Catalans Numbers – Part (2) Details 57:52 Catalan Numbers – Part (3), Sterling numbers of the 2nd kind Details 58:35 Difference Sequences Details 59:4 Sterling Numbers Details 59:16 Summary Details 18:8

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