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arXiv · 2502.21204

Halfspace Representations of Path Polytopes of Trees

Amer Goel·Aida Maraj·Alvaro Ribot
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Abstract

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

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Amer Goel, Aida Maraj, Alvaro Ribot. 2025-02-28. Halfspace Representations of Path Polytopes of Trees. https://arxiv.org/abs/2502.21204

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