Sign matrix polytopes from Young tableaux

TL;DR

This paper introduces new families of polytopes formed from sign matrices linked to Young tableaux, exploring their geometric properties and connections to existing matrix polytopes.

Contribution

It defines novel polytopes based on sign matrices associated with Young tableaux and analyzes their structural properties and relationships to known polytopes.

Findings

Characterization of vertices and facets of the new polytopes

Connections established between sign matrix polytopes and alternating sign matrix polytopes

Descriptions of inequality descriptions and face lattices

Abstract

Motivated by the study of polytopes formed as the convex hull of permutation matrices and alternating sign matrices, we define several new families of polytopes as convex hulls of sign matrices, which are certain {0,1,-1}-matrices in bijection with semistandard Young tableaux. We investigate various properties of these polytopes, including their inequality descriptions, vertices, facets, and face lattices, as well as connections to alternating sign matrix polytopes and transportation polytopes.