Dan Drake / Department of Mathematical Sciences / KAIST

information about my research

I finished my PhD at the University of Minnesota in 2006. Here’s my thesis, and here’s the known errata list.

associated Hermite polynomials

At FPSAC 2007 I gave a talk on the combinatorics of associated Hermite polynomials. I have slides from the talk, and a preprint of the paper is available at arXiv:0709.0987. The paper appeared in the European Journal of Combinatorics: doi:10.1016/j.ejc.2008.05.009 (here is citation info).

k-distant noncrossing matchings and set partitions

Jang Soo Kim and I have a preprint: k-distant crossings of matchings and set partitions, which was accepted as a poster at FPSAC 2009 and appears in the proceedings.

Higher-order matching polynomials and d-orthogonality

See arXiv:0909.1655. This paper was published in Advances in Applied Mathematics: doi:10.1016/j.aam.2009.12.008.

Bijections from weighted Dyck paths to Schröder paths

See arXiv:1006.1959. In the k-distant noncrossing matchings paper above, Jang Soo and I proved that little Schroeder paths are equal to the generating function for certain weighted Dyck paths; this paper presents a bijective proof of that fact and examines its consequences. This appeared in the Journal of Integer Sequences. I gave a talk on this bijection at the Korea Combinatorics Workshop at Yeungnam University; here are the slides. I also gave a talk on the bijection at the fall 2010 KMS meeting at Postech: here are those slides which are an improved version of the Yeungnam ones. The Sage demo I used is here.

I talked about this bijection at the KPP combinatorics seminar, in the larger context of the combinatorics of Chebyshev, Hermite, and Charlier orthogonal polynomials. Here are the slides.

Generating functions for plateaus in Motzkin paths

This is joint work with Ryan Gantner; see arXiv:1109.3273.