M-convexity of Grothendieck polynomials via bubbling

TL;DR

This paper introduces bubbling diagrams to analyze the support of Grothendieck polynomials for vexillary permutations, revealing M-convexity and connections to flagged Weyl modules, advancing combinatorial and algebraic understanding.

Contribution

It presents bubbling diagrams as a new tool to compute support and proves M-convexity of the homogenized Grothendieck polynomial support for vexillary permutations.

Findings

Support of top homogeneous component matches dual character of flagged Weyl module

Support of homogenized Grothendieck polynomial is M-convex

Bubbling diagrams effectively compute polynomial support

Abstract

We introduce bubbling diagrams and show that they compute the support of the Grothendieck polynomial of any vexillary permutation. Using these diagrams, we show that the support of the top homogeneous component of such a Grothendieck polynomial coincides with the support of the dual character of an explicit flagged Weyl module. We also show that the homogenized Grothendieck polynomial of a vexillary permutation has M-convex support.