# Combinatorics

IISc Bangalore Course , Prof. L. Sunil Chandran

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# 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

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

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# Lecture Details

Combinatorics by Dr. L. Sunil Chandran,Department of Computer Science and Engineering,IISc Bangalore.For more details on NPTEL visit httpnptel.ac.in

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