Séminaire Lotharingien de Combinatoire, 89B.7 (2023), 12 pp.
Yasuhide Numata, Yusuke Takahashi and Dai Tamaki
Faces of Directed Edge Polytopes
Abstract.
Given a finite quiver (directed graph) without loops and
multiedges, the convex hull of the column vector of the incidence
matrix is called the directed edge polytope and is an interesting
example of lattice polytopes.
In this article, we give a complete characterization of facets of the
directed edge polytope of an arbitrary finite quiver without loops and
multiedges in terms of the connectivity and the existence of a rank
function. Our result can be regarded as an extension of the result of
Higashitani et al. on facets of symmetric edge
polytopes to directed edge polytopes.
When the quiver in question has a rank function, we obtain a
characterization of faces of arbitrary dimensions.
This article is an extended abstract of the full paper at
arXiv:2203.14521.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
The following versions are available: