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Vasu Tewari: Divided symmetrization, Schubert polynomials and quasisymmetric functions

Time: Tue 2020-02-04 10.00 - 10.50

Lecturer: Vasu Tewari, University of Pennsylvania

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan

Abstract

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.

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Belongs to: Department of Mathematics
Last changed: Jan 31, 2020