Subdivisions of root polytopes and generalized tropical oriented matroids (Extended abstract)

TL;DR

This paper explores a generalization of tropical oriented matroids, establishing a bijection with subdivisions of root polytopes, which are specific sub-polytopes of a product of two simplices, advancing the understanding of their combinatorial structure.

Contribution

It introduces a new generalization of tropical oriented matroids and proves their correspondence with subdivisions of root polytopes, linking combinatorial and geometric concepts.

Findings

Established a bijection between generalized tropical oriented matroids and root polytope subdivisions.

Connected tropical combinatorics with geometric subdivisions of polytopes.

Extended the framework of tropical oriented matroids to a broader class of polytopes.

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.