We examine Eulerian polynomials and bubble sorting in Coxeter groups of type A, B, and D. In particular, we find nice statistics which compute the bubble sort complexity, which we use to refine the corresponding Eulerian polynomials. Recurrences for these refined Eulerian polynomials lead to new recurrences for the Eulerian polynomials of types B and D, and we give combinatorial proofs. We discuss how the type D recurrence in particular may lead to an alternate proof of a recently settled conjecture on the real rootedness of the type D Eulerian polynomials.
CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar
Thursday, March 20, 2014 - 2:30pm
Matt Hyatt
Lehigh University