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Combinatorics

Combinatorics. Instructor: Prof. Sunil Chandran, Department of Computer Science and Automation, IISc Bangalore. This course covers the topics typically covered in a first level combinatorics course. It introduces the elementary notions in combinatorics and presents the most elementary techniques in combinatorics - pigeonhole principle, inclusion-exclusion principle, recurrence relations and generating functions. (from nptel.ac.in)

Lecture 38 - Catalan Numbers Part 3, Stirling Numbers of the Second Kind

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Pigeonhole Principle

Lecture 01 - Pigeon Hole Principle, Part 1

Lecture 02 - Pigeonhole Principle, Part 2

Lecture 03 - Pigeonhole Principle, Part 3

Lecture 04 - Pigeonhole Principle, Part 4

Elementary Concepts

Lecture 05 - Elementary Concepts and Basic Counting Principles

Lecture 06 - Elementary Concepts; Binomial Theorem; Bijective Proofs Part 1

Lecture 07 - Bijective Proofs Part 2

Lecture 08 - Bijective Proofs Part 3; Properties of Binomial Coefficients; Combinatorial Identities

Lecture 09 - 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 - Stirling'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

Some Techniques

Lecture 17 - Double Counting Part 1

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

Recurrence Relations and Generating Functions

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

Special Numbers

Lecture 34 - Partition Number Part 2

Lecture 35 - Partition Number Part 3

Lecture 36 - Partition Number Part 4, Catalan Numbers Part 1

Lecture 37 - Catalan Numbers Part 2

Lecture 38 - Catalan Numbers Part 3, Stirling Numbers of the Second Kind

Lecture 39 - Difference Sequences

Lecture 40 - Stirling Numbers

Lecture 41 - Summary