Halfspace Representations of Path Polytopes of Trees
Combinatorics
2025-03-03 v1 Statistics Theory
Statistics Theory
Abstract
Given a tree , its path polytope is the convex hull of the edge indicator vectors for the paths between any two distinct leaves in . These polytopes arise naturally in polyhedral geometry and applications, such as phylogenetics, tropical geometry, and algebraic statistics. We provide a minimal halfspace representation of these polytopes. The construction is made inductively using toric fiber products.
Cite
@article{arxiv.2502.21204,
title = {Halfspace Representations of Path Polytopes of Trees},
author = {Amer Goel and Aida Maraj and Alvaro Ribot},
journal= {arXiv preprint arXiv:2502.21204},
year = {2025}
}
Comments
12 pages, 3 figures