Seminar Details
Cyclic Permutations, Shuffles, and Quasi-Symmetric Functions
- Start Date: February 4, 2021
- Event Start Time: 5:00 PM
- Event End Time: 6:00 PM
- Seminar Series: Experimental Math Seminar
- Presenter(s): Ron Adin - Bar-Ilan University
- Event Location: Online Event
- Event Presentation Link
- Event Additional Info: <p>Presented Via Zoom: <a href="https://rutgers.zoom.us/j/94346444480">https://rutgers.zoom.us/j/94346444480</a></p> <p> </p> <p>Password: 6564120420</p> <p> </p>
- Presentation Type: Stand Alone Presentation
- Abstract:
Richard Stanley proved that the distribution of descent number over all the shuffles of two permutations depends only on the descent numbers of the permutations.
We present an explicit cyclic analogue of this result. The tools used for the proof include a new cyclic counterpart of Gessels quasi-symmetric functions, an unusual ring homomorphism, and a mysterious binomial identity with an interesting history.
Based on joint work with Ira Gessel, Vic Reiner, and Yuval Roichman.