English

Halfspace Representations of Path Polytopes of Trees

Combinatorics 2025-03-03 v1 Statistics Theory Statistics Theory

Abstract

Given a tree TT, its path polytope is the convex hull of the edge indicator vectors for the paths between any two distinct leaves in TT. 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.

Keywords

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