# Triangulations of $Δ {n-1} imes Δ {d-1}$ and Tropical Oriented Matroids - Mathematics > Combinatorics

Triangulations of $Δ {n-1} imes Δ {d-1}$ and Tropical Oriented Matroids - Mathematics > Combinatorics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: Develin and Sturmfels showed that regular triangulations of $\Delta {n-1}\times \Delta {d-1}$ can be thought as tropical polytopes. Tropical orientedmatroids were defined by Ardila and Develin, and were conjectured to be inbijection with all subdivisions of $\Delta {n-1} \times \Delta {d-1}$. In thispaper, we show that any triangulation of $\Delta {n-1} \times \Delta {d-1}$encodes a tropical oriented matroid. We also suggest a new class ofcombinatorial objects that may describe all subdivisions of a bigger class ofpolytopes.

Autor: Suho Oh, Hwanchul Yoo

Fuente: https://arxiv.org/