Algebraic Combinatorics F9NFNE6HCH

URI	`m2://res/F9NFNE6HCH`
Kind	course
Creators	Amritanshu Prasad Prof. Sankaran Viswanath (instructor)
Date	2022-10-10
Scope	in

Expressions

e1: edition

Language	en
Date	2022-10-10

m1: page, IMSc (record). nptel 111106158
m2: page, 2022-10-10 (record). nptel 111106158

Contents

part 1: Week 0
session 1: Examples of Mobius Inversion
session 2: Partially Ordered Sets
session 3: Hasse Diagrams
session 4: Isomorphsms of Posets
session 5: Maximal, Minimal, Greatest, Least
session 6: Induced Subposets
session 7: Incidence Algebras
session 8: Inversion in Incidence Algebras
session 9: Mobius Inversion
session 10: Examples of Mobius Functions
session 11: Product Posets and their Mobius Functions
session 12: Opposite of a Poset
session 13: The Poset of Set Partitions
session 14: Connected Structures
part 2: Week 2
session 15: Lattices
session 16: Weisner's Theorem
session 17: The Lattice of Non-Crossing Partitions
session 18: The Canonical Product Decoposition for Intervals of Non-Crossing Partitions
session 19: The Mobius Function for Non-Crossing Partitions
session 20: Ideals in a Poset
session 21: Mobius Function of J(P)
session 22: Young's Lattice
session 23: Distributive Lattices
part 3: Week 3
session 24: Formal Power Series
session 25: The Necklace Problem
session 26: Combinatorial Classes
session 27: Sums, Products, and Sequences of Combinatorial Classes
session 28: Power Set, Multisets, and Sequences
session 29: A Little Dendrology
part 4: Week 4
session 30: Super Catalan/Little Schroeder numbers
session 31: Regular Languages
session 32: Finite Automata
session 33: The Pumping Lemma
session 34: The Dyck Language
part 5: Week 5
session 35: Permutations and their cycles
session 36: Permutation Groups
session 37: Orbits, fixed points, stabilizers
session 38: The orbit counting theorem
session 39: The Polya Enumeration Theorem
session 40: The Cycle Index Polynomials
session 41: Cycle Index of the Octahedral Group
session 42: Cycle Index of the Full Permutation Group
part 6: Week 6
session 43: Combinatorial Species
session 44: Generating Series of a Species
session 45: Cycle Index Series of a Species
session 46: Isomorphism of Species
session 47: Visualization of Species
session 48: Sum of Species
session 49: Product of Species
part 7: Week 7
session 50: Sums and Products: More Examples
session 51: Substitution of Species
session 52: Derivative of a Species
session 53: Powers and Seqeunces of Binomial Type
session 54: Pointing and Cayley's Theorem
session 55: R-enriched Trees
session 56: R-enriched Endofunctions
session 57: Lagrange Inversion Forumla
part 8: Week 8
session 58: Motivation for the LGV Lemma
session 59: Statement of the LGV Lemma
session 60: Nice Applications of the LGV Lemma
session 61: Sign-Reversing Involutions
session 62: Proof of the LGV Lemma
session 63: The Cauchy-Binet Formula
session 64: Symmetric polynomials: definition and examples
part 9: Week 9
session 65: Monomial symmetric polynomials
session 66: Elementary and Complete symmetric polynomials: part 1
session 67: Elementary and Complete symmetric polynomials: part 2
session 68: Alternating polynomials
session 69: Labelled abaci and alternants
session 70: Schur polynomials
part 10: Week 10
session 71: Pieri rule - statement and examples
session 72: Pieri rule - proof
session 73: The second Pieri rule
session 74: Semi-standard tableaux
session 75: Triangularity of Kostka matrix
part 11: Week 11
session 76: Monomial expansion of Schur
session 77: The RSK correspondence
session 78: Jacobi Trudi identities via LGV lemma
session 79: Formal ring of symmetric functions in infinitely many variables
part 12: Week 12
session 80: Generating functions for e, h
session 81: The power sum symmetric functions
session 82: The inner product and Cauchy identity
session 83: Monomial expansions and RSK
session 84: Skew Schur functions and the LR rule
part 13: Live Session
session 85: Live Session 04-02-2022

Catalogue records

nptel: 111106158 (manifestation)
nptel_video: 111106158 (manifestation)