# Algebraic Combinatorics

- Institution: IMSc
- Department: Mathematics
- Teacher: Prof. Amritanshu Prasad Prof. Sankaran Viswanath
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106158)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106158)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Examples of Mobius Inversion](https://invisiblenetwork.ai/learn/nptel/111106158/a9a143ce6310) (Video)
2. [Partially Ordered Sets](https://invisiblenetwork.ai/learn/nptel/111106158/c774ea7aa503) (Video)
3. [Hasse Diagrams](https://invisiblenetwork.ai/learn/nptel/111106158/c4ed3ac9277f) (Video)
4. [Isomorphsms of Posets](https://invisiblenetwork.ai/learn/nptel/111106158/bab944e6111d) (Video)
5. [Maximal, Minimal, Greatest, Least](https://invisiblenetwork.ai/learn/nptel/111106158/50ba4f1b3e1c) (Video)
6. [Induced Subposets](https://invisiblenetwork.ai/learn/nptel/111106158/943a9070aaf9) (Video)
7. [Incidence Algebras](https://invisiblenetwork.ai/learn/nptel/111106158/05c69497f1ab) (Video)
8. [Inversion in Incidence Algebras](https://invisiblenetwork.ai/learn/nptel/111106158/ee96f6cf1586) (Video)
9. [Mobius Inversion](https://invisiblenetwork.ai/learn/nptel/111106158/c3d7bdfd9568) (Video)
10. [Examples of Mobius Functions](https://invisiblenetwork.ai/learn/nptel/111106158/1a23d91c4d8c) (Video)
11. [Product Posets and their Mobius Functions](https://invisiblenetwork.ai/learn/nptel/111106158/d168a8522973) (Video)
12. [Opposite of a Poset](https://invisiblenetwork.ai/learn/nptel/111106158/1f6f5ac37bdb) (Video)
13. [The Poset of Set Partitions](https://invisiblenetwork.ai/learn/nptel/111106158/b09d8d2cc791) (Video)
14. [Connected Structures](https://invisiblenetwork.ai/learn/nptel/111106158/a9ab1c25d903) (Video)
15. [Lattices](https://invisiblenetwork.ai/learn/nptel/111106158/636e1b63c70d) (Video)
16. [Weisner's Theorem](https://invisiblenetwork.ai/learn/nptel/111106158/3579ead82757) (Video)
17. [The Lattice of Non-Crossing Partitions](https://invisiblenetwork.ai/learn/nptel/111106158/9977f381fbbd) (Video)
18. [The Canonical Product Decoposition for Intervals of Non-Crossing Partitions](https://invisiblenetwork.ai/learn/nptel/111106158/6eaec150de1f) (Video)
19. [The Mobius Function for Non-Crossing Partitions](https://invisiblenetwork.ai/learn/nptel/111106158/e48e2b4da1ec) (Video)
20. [Ideals in a Poset](https://invisiblenetwork.ai/learn/nptel/111106158/3caf4122b8b2) (Video)
21. [Mobius Function of J(P)](https://invisiblenetwork.ai/learn/nptel/111106158/9f37e8bc25f9) (Video)
22. [Young's Lattice](https://invisiblenetwork.ai/learn/nptel/111106158/74a37772fdf4) (Video)
23. [Distributive Lattices](https://invisiblenetwork.ai/learn/nptel/111106158/fe542602ff0b) (Video)
24. [Formal Power Series](https://invisiblenetwork.ai/learn/nptel/111106158/d45180b1ffa7) (Video)
25. [The Necklace Problem](https://invisiblenetwork.ai/learn/nptel/111106158/3ef520b7a75f) (Video)
26. [Combinatorial Classes](https://invisiblenetwork.ai/learn/nptel/111106158/0b41e7d9ac41) (Video)
27. [Sums, Products, and Sequences of Combinatorial Classes](https://invisiblenetwork.ai/learn/nptel/111106158/e603c1930d64) (Video)
28. [Power Set, Multisets, and Sequences](https://invisiblenetwork.ai/learn/nptel/111106158/02a9c835a175) (Video)
29. [A Little Dendrology](https://invisiblenetwork.ai/learn/nptel/111106158/e677346c8f00) (Video)
30. [Super Catalan/Little Schroeder numbers](https://invisiblenetwork.ai/learn/nptel/111106158/96de782c38a9) (Video)
31. [Regular Languages](https://invisiblenetwork.ai/learn/nptel/111106158/0340f2fe2fa3) (Video)
32. [Finite Automata](https://invisiblenetwork.ai/learn/nptel/111106158/844d1e4c3c59) (Video)
33. [The Pumping Lemma](https://invisiblenetwork.ai/learn/nptel/111106158/56787ccb1a03) (Video)
34. [The Dyck Language](https://invisiblenetwork.ai/learn/nptel/111106158/3b21f0b87089) (Video)
35. [Permutations and their cycles](https://invisiblenetwork.ai/learn/nptel/111106158/0278e932fed0) (Video)
36. [Permutation Groups](https://invisiblenetwork.ai/learn/nptel/111106158/757c6679634c) (Video)
37. [Orbits, fixed points, stabilizers](https://invisiblenetwork.ai/learn/nptel/111106158/ec1fc6dc2054) (Video)
38. [The orbit counting theorem](https://invisiblenetwork.ai/learn/nptel/111106158/11b4e009e6aa) (Video)
39. [The Polya Enumeration Theorem](https://invisiblenetwork.ai/learn/nptel/111106158/977b42db136c) (Video)
40. [The Cycle Index Polynomials](https://invisiblenetwork.ai/learn/nptel/111106158/936a6b442f04) (Video)
41. [Cycle Index of the Octahedral Group](https://invisiblenetwork.ai/learn/nptel/111106158/68a08eb5d408) (Video)
42. [Cycle Index of the Full Permutation Group](https://invisiblenetwork.ai/learn/nptel/111106158/797db68ff5c8) (Video)
43. [Combinatorial Species](https://invisiblenetwork.ai/learn/nptel/111106158/ab8401f167ee) (Video)
44. [Generating Series of a Species](https://invisiblenetwork.ai/learn/nptel/111106158/9603e77d822d) (Video)
45. [Cycle Index Series of a Species](https://invisiblenetwork.ai/learn/nptel/111106158/3ab4f99c1528) (Video)
46. [Isomorphism of Species](https://invisiblenetwork.ai/learn/nptel/111106158/d150b245c9e8) (Video)
47. [Visualization of Species](https://invisiblenetwork.ai/learn/nptel/111106158/bef5a4e2fa46) (Video)
48. [Sum of Species](https://invisiblenetwork.ai/learn/nptel/111106158/bc6e42092804) (Video)
49. [Product of Species](https://invisiblenetwork.ai/learn/nptel/111106158/bc3c28c9e81a) (Video)
50. [Sums and Products: More Examples](https://invisiblenetwork.ai/learn/nptel/111106158/4770b71648ca) (Video)
51. [Substitution of Species](https://invisiblenetwork.ai/learn/nptel/111106158/4e3237893e1e) (Video)
52. [Derivative of a Species](https://invisiblenetwork.ai/learn/nptel/111106158/7b293b8a661c) (Video)
53. [Powers and Seqeunces of Binomial Type](https://invisiblenetwork.ai/learn/nptel/111106158/beab7b05d25a) (Video)
54. [Pointing and Cayley's Theorem](https://invisiblenetwork.ai/learn/nptel/111106158/c7f21bf666eb) (Video)
55. [R-enriched Trees](https://invisiblenetwork.ai/learn/nptel/111106158/dc1d4752a17c) (Video)
56. [R-enriched Endofunctions](https://invisiblenetwork.ai/learn/nptel/111106158/0a0963240003) (Video)
57. [Lagrange Inversion Forumla](https://invisiblenetwork.ai/learn/nptel/111106158/8dc62820e5e1) (Video)
58. [Motivation for the LGV Lemma](https://invisiblenetwork.ai/learn/nptel/111106158/59cd3c4e5cb3) (Video)
59. [Statement of the LGV Lemma](https://invisiblenetwork.ai/learn/nptel/111106158/70903f79d8d8) (Video)
60. [Nice Applications of the LGV Lemma](https://invisiblenetwork.ai/learn/nptel/111106158/0a629101a03a) (Video)
61. [Sign-Reversing Involutions](https://invisiblenetwork.ai/learn/nptel/111106158/e075561ddaee) (Video)
62. [Proof of the LGV Lemma](https://invisiblenetwork.ai/learn/nptel/111106158/6f3e7b4cfc65) (Video)
63. [The Cauchy-Binet Formula](https://invisiblenetwork.ai/learn/nptel/111106158/2d4efad53ef4) (Video)
64. [Symmetric polynomials: definition and examples](https://invisiblenetwork.ai/learn/nptel/111106158/ad34a17d1982) (Video)
65. [Monomial symmetric polynomials](https://invisiblenetwork.ai/learn/nptel/111106158/6fa92dac1695) (Video)
66. [Elementary and Complete symmetric polynomials: part 1](https://invisiblenetwork.ai/learn/nptel/111106158/0f94e4a5beba) (Video)
67. [Elementary and Complete symmetric polynomials: part 2](https://invisiblenetwork.ai/learn/nptel/111106158/7a671b236b7d) (Video)
68. [Alternating polynomials](https://invisiblenetwork.ai/learn/nptel/111106158/2ceb2ec4834e) (Video)
69. [Labelled abaci and alternants](https://invisiblenetwork.ai/learn/nptel/111106158/704c388ac5f4) (Video)
70. [Schur polynomials](https://invisiblenetwork.ai/learn/nptel/111106158/609c59321a5e) (Video)
71. [Pieri rule - statement and examples](https://invisiblenetwork.ai/learn/nptel/111106158/09e5ae79241a) (Video)
72. [Pieri rule - proof](https://invisiblenetwork.ai/learn/nptel/111106158/275f8e909114) (Video)
73. [The second Pieri rule](https://invisiblenetwork.ai/learn/nptel/111106158/34143e8978c6) (Video)
74. [Semi-standard tableaux](https://invisiblenetwork.ai/learn/nptel/111106158/6b54d88dd2df) (Video)
75. [Triangularity of Kostka matrix](https://invisiblenetwork.ai/learn/nptel/111106158/c90ac72d937d) (Video)
76. [Monomial expansion of Schur](https://invisiblenetwork.ai/learn/nptel/111106158/0f1feedebca1) (Video)
77. [The RSK correspondence](https://invisiblenetwork.ai/learn/nptel/111106158/57aa4a7fee0f) (Video)
78. [Jacobi Trudi identities via LGV lemma](https://invisiblenetwork.ai/learn/nptel/111106158/fb9ed9cc41b5) (Video)
79. [Formal ring of symmetric functions in infinitely many variables](https://invisiblenetwork.ai/learn/nptel/111106158/5a030fab86e1) (Video)
80. [Generating functions for e, h](https://invisiblenetwork.ai/learn/nptel/111106158/e3d433ab0f65) (Video)
81. [The power sum symmetric functions](https://invisiblenetwork.ai/learn/nptel/111106158/3ec57f973559) (Video)
82. [The inner product and Cauchy identity](https://invisiblenetwork.ai/learn/nptel/111106158/559a1b4dfa68) (Video)
83. [Monomial expansions and RSK](https://invisiblenetwork.ai/learn/nptel/111106158/6d99186701f7) (Video)
84. [Skew Schur functions and the LR rule](https://invisiblenetwork.ai/learn/nptel/111106158/528b15f56f4f) (Video)
85. [Live Session 04-02-2022](https://invisiblenetwork.ai/learn/nptel/111106158/a9a143ce6310-2) (Video)