Please join the Department of Mathematics and Statistics on Monday, September 20th at 4:40pm in Votey Hall 209 for a fascinating combinatorics seminar featuring Dartmouth College's, Professor and Department Chair, Sergi Elizalde.
Descents on Quasi-Stirling Permutations
Professor Sergi Elizalde, Dartmouth College
Monday, September 20th, 4:40 PM, Votey Hall 209
Abstract: Stirling permutations were introduced by Gessel and Stanley to give a combinatorial interpretation of certain polynomials related to Stirling numbers, which count set partitions with a given number of blocks. A natural extension of Stirling permutations are quasi-Stirling permutations, which are in bijection with labeled rooted plane trees. Archer et al. introduced these permutations, and conjectured that there are $(n+1)^{n-1}$ quasi-Stirling permutations of size $n$ having $n$ descents.
In this talk we will discuss how to prove this conjecture. More generally, we will show that the generating function for quasi-Stirling permutations by the number of descents satisfies a beautiful equation involving the Eulerian polynomials. We will show that some of the properties of descents on usual permutations and on Stirling permutations have an analogue for quasi-Stirling permutations.