NOC:Algebraic Combinatorics

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