1 8/25Mo: introduction (overview of topics)
Topic 1: Enumeration
2 8/27We: Hook-Length Formula
3 8/29Fr: RSK Correspondence, Schensted's Thm, Planarization
4 9/03We: Jeu de Taquin, Greene's Theorem
5 9/05Fr: Lagrange Inversion, motivated by Cayley's Formula
6 9/08Mo: polya review, bulgarian solitaire, ordinary exponential formula
7 9/10We: isom classes of rooted trees, power group enumeration
8 9/12Fr: snake oil examples, WZ pairs
9 9/15Mo: hypergeometric series, reluctant functions, binomial sequences
10 9/17We: Shift-Invariant operators, expansion theorem
11 9/19Fr: umbral algebra isomorphism theorem, idea of connection coeffs
Topic 2: Ramsey theory
12 9/22Mo: pigeonhole principle (two squares, generalized chess player)
13 9/24We: Stanley-Wilf conjecture, infinite Ramsey intro
14 9/26Fr: infinite Ramsey theorem, compactness, intro canonical Ramsey
15 9/29Mo: canonical Ramsey theorem, pattern Ramsey numbers
16 10/01We: anti-Ramsey numbers (cycles), intro to Schur/Rado/VdWaerden
17 10/03Fr: Van der Waerden's Theorem
18 10/06Mo: apply VdW to Rado's regular equations, start parameter Ramsey
19 10/08We: chromatic Ramsey number, degree Ramsey number
20 10/10Fr: more degree Ramsey, on-line chromatic Ramsey number
21 10/13Mo: more on-line chromatic, forests, triangles & outerplanar,
on-line degree Ramsey lower bound
22 10/15We: odr for trees, consistent Painter theorem
23 10/17Fr: intro to game chromatic number
24 10/20Mo: game chromatic number at most 18 for planar graphs
Topic 3: Design theory
25 10/22We: Difference sets, the Multiplier Theorem
26 10/24Fr: Steiner triple systems, resolvable designs
27 10/27Mo: pairwise-balanced designs, orthogonal arrays, disproof of Euler
conjecture
28 10/29We: Baranyai's Theorem, covering designs, idea of Rodl nibble
29 10/31Fr: tools for Wilson's Theorem
30 11/03Mo: more pieces of Wilson's Theorem
Topic 4: Geometry, etc.
31 11/05We: Sperner's Lemma, Brouwer Fixed-Point Theorem, bandwidth
32 11/07Fr: equivalence of Sperner, Connector, Hex, Pouzet, Brouwer
33 11/10Mo: Tucker's Combinatorial Lemma
34 11/12We: Borsuk-Ulam Theorem, Kneser Conjecture
35 11/14Fr: Gale's Lemma, Schrijver graphs, Ham Sandwich & applications
36 11/17Mo: disproof of Borsuk's Conjecture
Topic 5: Algebraic methods
36 11/17Mo: RayChaudhuri-Wilson Theorem
37 11/19We: Oddtown Theorem, two-distance sets, large t-uniform family
with small intersections
38 11/21Fr: Nonuniform modular RW Theorem, application to Ramsey
construction
39 12/1Mo: Omitted-Intersection Theorem, unit-distance graph, modular Snevily Theorem
40 12/3We: combinatorial nullstellensatz, Cauchy-Davenport Theorem
41 12/5Fr: Chevalley-Warning Theorem, transversal of hyperplanes in cubes,
existence of regular subgraphs
42 12/8Mo: ex(n;k-regular), generalized factors
43 12/10We: generalized factors, stunted trees, antimagic graphs