Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Amritanshu Prasad, Prof. Sankaran Viswanath
NPTEL Co-ordinating Institute : IIT Madras
NPTEL Lecture Count : 84
NPTEL Course Size : 3.7 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Examples of Mobius Inversion
Lecture 2 - Partially Ordered Sets
Lecture 3 - Hasse Diagrams
Lecture 4 - Isomorphsms of Posets
Lecture 5 - Maximal, Minimal, Greatest, Least
Lecture 6 - Induced Subposets
Lecture 7 - Incidence Algebras
Lecture 8 - Inversion in Incidence Algebras
Lecture 9 - Mobius Inversion
Lecture 10 - Examples of Mobius Functions
Lecture 11 - Product Posets and their Mobius Functions
Lecture 12 - Opposite of a Poset
Lecture 13 - The Poset of Set Partitions
Lecture 14 - Connected Structures
Lecture 15 - Lattices
Lecture 16 - Weisner's Theorem
Lecture 17 - The Lattice of Non-Crossing Partitions
Lecture 18 - The Canonical Product Decoposition for Intervals of Non-Crossing Partitions
Lecture 19 - The Mobius Function for Non-Crossing Partitions
Lecture 20 - Ideals in a Poset
Lecture 21 - Mobius Function of J(P)
Lecture 22 - Young's Lattice
Lecture 23 - Distributive Lattices
Lecture 24 - Formal Power Series
Lecture 25 - The Necklace Problem
Lecture 26 - Combinatorial Classes
Lecture 27 - Sums, Products, and Sequences of Combinatorial Classes
Lecture 28 - Power Set, Multisets, and Sequences
Lecture 29 - A Little Dendrology
Lecture 30 - Super Catalan/Little Schroeder numbers
Lecture 31 - Regular Languages
Lecture 32 - Finite Automata
Lecture 33 - The Pumping Lemma
Lecture 34 - The Dyck Language
Lecture 35 - Permutations and their cycles
Lecture 36 - Permutation Groups
Lecture 37 - Orbits, fixed points, stabilizers
Lecture 38 - The orbit counting theorem
Lecture 39 - The Polya Enumeration Theorem
Lecture 40 - The Cycle Index Polynomials
Lecture 41 - Cycle Index of the Octahedral Group
Lecture 42 - Cycle Index of the Full Permutation Group
Lecture 43 - Combinatorial Species
Lecture 44 - Generating Series of a Species
Lecture 45 - Cycle Index Series of a Species
Lecture 46 - Isomorphism of Species
Lecture 47 - Visualization of Species
Lecture 48 - Sum of Species
Lecture 49 - Product of Species
Lecture 50 - Sums and Products: More Examples
Lecture 51 - Substitution of Species
Lecture 52 - Derivative of a Species
Lecture 53 - Powers and Seqeunces of Binomial Type
Lecture 54 - Pointing and Cayley's Theorem
Lecture 55 - R-enriched Trees
Lecture 56 - R-enriched Endofunctions
Lecture 57 - Lagrange Inversion Forumla
Lecture 58 - Motivation for the LGV Lemma
Lecture 59 - Statement of the LGV Lemma
Lecture 60 - Nice Applications of the LGV Lemma
Lecture 61 - Sign-Reversing Involutions
Lecture 62 - Proof of the LGV Lemma
Lecture 63 - The Cauchy-Binet Formula
Lecture 64 - Symmetric polynomials: definition and examples
Lecture 65 - Monomial symmetric polynomials
Lecture 66 - Elementary and Complete symmetric polynomials - Part 1
Lecture 67 - Elementary and Complete symmetric polynomials - Part 2
Lecture 68 - Alternating polynomials
Lecture 69 - Labelled abaci and alternants
Lecture 70 - Schur polynomials
Lecture 71 - Pieri Rule - Statement and Examples
Lecture 72 - Pieri Rule - Proof
Lecture 73 - The second Pieri rule
Lecture 74 - Semi-standard tableaux
Lecture 75 - Triangularity of Kostka matrix
Lecture 76 - Monomial expansion of Schur
Lecture 77 - The RSK correspondence
Lecture 78 - Jacobi Trudi identities via LGV lemma
Lecture 79 - Formal ring of symmetric functions in infinitely many variables
Lecture 80 - Monomial expansions and RSK
Lecture 81 - Generating functions for e, h
Lecture 82 - The power sum symmetric functions
Lecture 83 - The inner product and Cauchy identity
Lecture 84 - Skew Schur functions and the LR rule