combinatorics

Subdivisions of root polytopes, generalized tropical oriented matroids, and generalized matching ensembles

arXiv:2603.08539

summary

The paper extends tropical oriented matroids and proves they correspond bijectively to subdivisions of root polytopes (sub‑polytopes of a product of two simplices), and also generalizes a matching‑based combinatorial model for triangulations.

Abstract

We study a generalization of tropical oriented matroids by Ardila and Develin, and show that they are in bijection with subdivisions of root polytopes, which are sub-polytopes of a product of two simplices. We also study a generalization of a matching-based combinatorial model by Oh and Yoo in the special case of triangulations.

20 pages, 7 figures. This is the full version of V1

Topics & keywords

#tropical oriented matroids#root polytopes#subdivisions#matching ensembles#triangulationstropical oriented matroidsroot polytopesubdivision bijectionproduct of simplicesmatching ensemblestriangulationcombinatorial geometry
Subdivisions of root polytopes, generalized tropical oriented matroids, and generalized matching ensembles · wovepaper