On nu Faces of Partial Alternating Sign Matrix Polytopes

Abstract

We define and study the $(\nu /\lambda )$-partial alternating sign matrix polytope, motivated by connections to the Chan-Robbins-Yuen polytope and the $\nu$-Tamari lattice. We determine the inequality description and show this polytope is a face of the partial alternating sign matrix polytope of [Heuer, Striker 2022]. We show that the $(\nu /\lambda )$-partial ASM polytope is an order polytope and a flow polytope.

15 pages, 8 figures