Math 118
Combinatorics
Last updated June 27, 2016 13:25:41 EDT
Each student is expected to give an in-class presentation on a topic of their choice. You can work individually, but for the longer papers
it is recommended that you work in small groups. Each of you should speak for about 30 minutes, although this is flexible.
Below is a list of suggested topics (more will be added as the course progresses).
You are more than welcome to find a topic not listed here; for example, you can present a combinatorics paper reasonably related to the course from a journal of your choice. Just check with me first.
A few suggested topics for student presentations
- (Taken by Jenny) The enumeration of lecture hall partitions.
Suggested references: [AE], [M. Bousquet-Melou, K. Eriksson, Lecture hall partitions, Ramanujan J. 1 (1997), no. 1, 101-111],
[A.J. Yee, On the combinatorics of lecture hall partitions, Ramanujan J. 5 (2001), no. 3, 247-262].
- (Taken by Tim and Kassie) [C. Boulet and I. Pak, A combinatorial proof of the Rogers-Ramanujan identities, J. Combin. Theory Ser. A 113 (2006), 1019-1030].
- Ramanujan's congruences for p(n).
See references in [G. Andrews, K. Ono, Ramanujan's congruences and Dyson's crank, Proc. NAS USA 102, 15277].
- (Taken by Jonathan) Determinants, nonintersecting paths, and Young tableaux. Sections 5-7 of [I. Gessel, G. Viennot, Binomial determinants, paths, and hook length formulae, Adv. in Math. 58 (1985), 300-321].
- (Taken by Eva) A bijection between k-triangulations and k-tuples of non-intersecting Dyck paths.
Suggested reference: [L. Serrano, C. Stump, Maximal fillings of moon polyominoes, simplicial complexes, and Schubert polynomials, Electron. J. Combin. 19 (2012), P16].
- (Taken by Megan) The alternating sign matrix conjecture.
Suggested references: [Br], [G. Kuperberg, Another proof of the alternating sign matrix conjecture, Internat. Math. Res. Notices 1996, 139-150].
- Promotion and rowmotion. [J. Striker, N. Williams, Promotion and rowmotion, European J. Combin. 33 (2012), 1919-1942].
- [M. Ciucu, Enumeration of Lozenge Tilings of Punctured Hexagons, J. of Combin. Theory Ser. A 83 (1998), 268-272].
- (Taken by Seth) A combinatorial proof of the unimodality of the q-binomial coefficients.
Suggested reference: [D. Zeilberger, Kathy O'Hara's constructive proof of the unimodality of the Gaussian Polynomials, {\it The American Mathematical Monthly} 96, 590-602].
- (Taken by David) Generalized associahedra and permutohedra.
Suggested reference: [A. Postnikov, Permutohedra, associahedra, and beyond, Int. Math. Res. Not. IMRN 2009, 1026-1106].
Last updated June 27, 2016 13:25:41 EDT