Math Seminar Series
(Conferences / Seminars / Lectures)
Sergi Elizalde Dartmouth College more information...
The seminar is titled "Descents on quasi-Stirling permutations."
Contact Bruce E Sagan (firstname.lastname@example.org) 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 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 prove this conjecture. More generally, we give the generating function for quasi-Stirling 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 quasi-Stirling permutations. Finally, we extend our results to a one-parameter family of permutations, called k-quasi-Stirling permutations, which are in bijection with certain decorated trees.