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Course10610805141 lectures

Combinatorics

Dr. L. Sunil Chandran · IISc Bangalore

Start with lecture 1 At NPTEL

Lectures

Pigeon hole Principle

  1. Pigeon hole principle - (Part 1) Video
  2. Pigeon hole principle - (Part 2) Video
  3. Pigeon hole principle - (Part 3) Video
  4. Pigeon hole principle - (Part 4) Video

Elementary Concepts

  1. Elementary concepts and basic counting principles Video
  2. Elementary concepts; Binomial theorem; Bijective proofs - Part (1) Video
  3. Bijective proofs – Part (2) Video
  4. Bijective proofs - Part (3); Properties of binomial coefficients; Combinatorial identities - Part (1) Video
  5. Combinatorial identities - Part (2); Permutations of multisets – Part (1) Video
  6. Permutations of multisets – Part (2) Video
  7. Multinomial Theorem, Combinations of Multisets – Part (1) Video
  8. Combinations of Multisets - Part (2) Video
  9. Combinations of Multisets – Part (3), Bounds for binomial coefficients Video
  10. Sterling’s Formula, Generalization of Binomial coefficients - Part (1) Video
  11. Generalization of Binomial coefficients - Part (2) Video
  12. Generalization of Binomial coefficients - Part (3); Double counting - Part (1) Video

Some Techniques

  1. Double counting - Part (2) Video
  2. Hall’s Theorem for regular bipartite graphs; Inclusion exclusion principle - Part (1) Video
  3. Inclusion exclusion principle - Part (2) Video
  4. Inclusion exclusion principle - Part (3) Video
  5. Inclusion exclusion principle - Part (4) Video
  6. Inclusion exclusion principle - Part (5) Video

Recurrence relations and generating functions

  1. Recurrence Relations - Part (1) Video
  2. Recurrence Relations - Part (2) Video
  3. Recurrence Relations - Part (3) Video
  4. Recurrence Relations - Part (4) Video
  5. Recurrence Relations - Part (5) Video
  6. Generating functions - Part (1) Video
  7. Generating functions - Part (2) Video
  8. Solving recurrence relations using generating functions - Part (1) Video
  9. Solving recurrence relations using generating functions - Part (2) Video
  10. Exponential generating functions - Part (1) Video
  11. Exponential generating functions - Part (2), Partition Number - Part (1) Video

Special numbers

  1. Partition Number - Part (2) Video
  2. Partition Number - Part (3) Video
  3. Partition Number - Part (4); Catalan Numbers - Part (1) Video
  4. Catalans Numbers - Part (2) Video
  5. Catalan Numbers - Part (3), Sterling numbers of the 2nd kind Video
  6. Difference Sequences Video
  7. Sterling Numbers Video
  8. Summary Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Computer Science and Engineering
Teacher
Dr. L. Sunil Chandran
Level
Undergraduate
Language
English
Subjects
Computer science, Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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