Affiliation: North Carolina State University
Title Of Talk: An Overview of Lecture Hall Partitions
Abstract: Lecture hall partitions were introduced by Bousquet Mélou and Eriksson in 1997. They gained attention because of their strikingly simple generating function and their connection to Euler's partition theorem. In the time since, lecture hall partitions and their generalizations have been shown to be interesting structures with applications in combinatorics and number theory. Surprising connections have surfaced with, for example, generalizations of Euler's partition theorem, overpartitions, Göllnitz's little partition theorems, permutation statistics, Eulerian polynomials, Ehrhart theory, inversion sequences, the real-rootedness of descent polynomials of finite Coxeter groups, multiset permutations, Gorenstein cones and self-reciprocal polynomials, the restricted Eulerian polynomials of Chung and Graham, integer partitions with even indexed parts even, and pattern avoidance in permutations. We give an overview of these connections and mention some recent results.
Last update made Tue Feb 9 06:55:04 PST 2016.