Vasu Tewari: Divided symmetrization, Schubert polynomials and quasisymmetric functions
Time: Tue 2020-02-04 10.00 - 10.50
Lecturer: Vasu Tewari, University of Pennsylvania
The procedure of divided symmetrization was introduced by Alex Postnikov in the context of computing volume polynomials of various classes of permutahedra. This procedure takes a multivariate polynomial as input and outputs a scalar, which in many cases is a combinatorially interesting quantity. In this talk, I will describe how performing divided symmetrization is equivalent to reducing multivariate polynomials modulo the ideal generated by the homogeneous quasi-symmetric polynomials of positive degree in a fixed number of variables. The special case of divided symmetrizing Schubert polynomials will serve as the main motivation. This is joint work with Philippe Nadeau at Institut Camille Jordan.