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 and Combinatorial Games

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: Topological methods

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