Student presentations
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 also 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.
Once you have chosen a topic, let me know so that I can mark it as
taken.
A few suggested topics for student presentations
- (Taken by Justin) Unimodality of the Eulerian polynomials.
Thm 5.6 in [Foata, Schutzenberger, Theorie geometrique des polynomes euleriens] if you want to read the original and don't mind French, or Thm 3 in [Petersen, arxiv.org/abs/1209.6273]
for a proof in English that uses "valley-hopping".
- (Taken by Harsh) Min-max trees and the cd-index.
[EC, Section 1.6.3]
- A combinatorial proof of the unimodality of the q-binomial coefficients.
[D. Zeilberger, Kathy O'Hara's constructive proof of the unimodality of the Gaussian Polynomials, The American Mathematical Monthly 96, 590-602].
- (Taken by Laura) The enumeration of lecture hall partitions.
[AE], [M. Bousquet-Melou and K. Eriksson, Lecture hall partitions, Ramanujan J. 1 (1997), no. 1, 101-111].
- (Taken by Doug and Melanie) More on lecture hall partitions.
[AE], [A.J. Yee, On the combinatorics of lecture hall partitions, Ramanujan J. 5 (2001), no. 3, 247-262].
- Ramanujan's congruences for p(n).
See references in [G. Andrews and K. Ono, Ramanujan's congruences and Dyson's crank, Proc. NAS USA 102, 15277].
- (Taken by Juan and Emma) A combinatorial proof of the Rogers-Ramanujan identities.
[C. Boulet and I. Pak, A combinatorial proof of the Rogers-Ramanujan identities, J. Combin. Theory Ser. A 113 (2006), 1019-1030].
- (Taken by Lizzie) A probabilistic proof of the hook-length formula.
[Greene, Nijenhuis and Wilf, A probabilistic proof of a formula for the number of Young tableaux of a given shape, Adv. in Math. 31 (1979) 104-109].
- (Taken by Tim) A bijective proof of the hook-length formula.
[Novelli, Pak and Stoyanovskii, A direct bijective proof of the hook-length formula, Disc. Math. Comp Sci. 1 (1997), 53-67].
- (Taken by Kate) Viennot's geometric construction and the symmetry of RSK.
[Section 3.6 of Sagan, The Symmetric Group, Springer].
- (Taken by Sarah) The alternating sign matrix conjecture.
[Br], [G. Kuperberg, Another proof of the alternating sign matrix conjecture, Internat. Math. Res. Notices 1996, 139-150],
[D. Bressoud and J. Propp, How the Alternating Sign Matrix Conjecture Was Solved, Notices of the AMS 46 (1999), 637-646].
- The Edelman-Greene correspondence.
[P. Edelman and C. Greene, Balanced tableaux, Adv. Math. 62 (1987), 42-99], [Felsner, The Skeleton of a Reduced Word and a Correspondence of Edelman and Greene, Elec. J. Combin. 8 (2001), #R10].
- (Taken by Chris) The expected number of corners in a lattice path.
[M. Chan, S. Haddadan, S. Hopkins and L. Moci, The expected jaggedness of order ideals, arxiv.org/abs/1507.00249].
- Bijections for plane partitions and non-intersecting lattice paths.
[Z. Hamaker, R. Patrias, O. Pechenik and N. Williams, Doppelgängers: Bijections of Plane Partitions, arxiv.org/abs/1602.05535].
Last updated August 11, 2020 16:04:36 EDT