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.

Gelfand--Tsetlin polytopes are prominent objects in algebraic combinatorics. The number of integer points of the Gelfand--Tsetlin polytope ${GT}(\lambda)$ is equal to the dimension of the corresponding irreducible representation of $GL(n)$. It is well known that the Gelfand--Tsetlin polytope is both a marked order polytope and a flow polytope. In this paper, we draw corollaries from this result and establish a general theory connecting marked order polytopes and flow polytopes.