Combinatorics Seminar

Grothendieck polynomials are polynomials in n variables, indexed by permutations of n elements. They encode the K-theory of the flag variety, and their lowest degree terms encode the cohomology of the flag variety. We study the highest degree part of Grothendieck polynomials, which should be related to the Castelnuovo-Mumford regularity of matrix Schubert varieties. We give a simple combinatorial rule for computing the degree of this highest degree part and show that, while there are n! many permutations, the number of highest degree parts (up to scalar multiple) is only the n-th Bell number. On the way, we discover surprising new properties of the classical major index statistic.

Joint work with Oliver Pechenik and Anna Weigandt. Speaker(s): David Speyer (University of Michigan)