Wednesday, January 20, 2021
3:00pm to 3:50pm


Math Seminar Series
(Conferences / Seminars / Lectures)
Sergi Elizalde Dartmouth College
The seminar is titled "Descents on quasiStirling permutations."
Contact Bruce E Sagan (bsagan@msu.edu) for more information.
Stirling permutations were introduced by Gessel and Stanley to give a combinatorial interpretation of certain polynomials related to Stirling numbers. A very natural extension of Stirling permutations are quasiStirling 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 quasiStirling permutations of size n having n descents. In this talk we prove this conjecture. More generally, we give the generating function for quasiStirling permutations by the number of descents, which turns out to satisfy a beautiful equation involving Eulerian polynomials. We show that some of the properties of descents on usual permutations and on Stirling permutations have an analogue for quasiStirling permutations. Finally, we extend our results to a oneparameter family of permutations, called kquasiStirling permutations, which are in bijection with certain decorated trees. more information...
