Per Alexandersson: The Schur expansion of skew specialized Macdonald polynomials

Time: Wed 2019-06-05 10.15 - 11.00

Lecturer: Per Alexandersson

Location: Room 3418, Lindstedtsvägen 25. Department of Mathematics, KTH

Abstract: We use a variant of RSK to give the Schur expansion of a
certain generalization of Macdonald polynomials.This family is closely related to LLT polynomials, for which there is
still no combinatorial proof of Schur positivity.

If there is time, we also give a new positive formula for
Touchard-Riordan polynomials, which reveals a surprising connection with rook-theory and acyclic
orientations of unit-interval graphs.

This is joint work with Joakim Uhlin.