Oriented Matroids from Triangulations of Products of Simplices
Abstract
We introduce a construction of oriented matroids from a triangulation of a product of two simplices. For this, we use the structure of such a triangulation in terms of polyhedral matching fields. The oriented matroid is composed of compatible chirotopes on the cells in a matroid subdivision of the hypersimplex, which might be of independent interest. In particular, we generalize this using the language of matroids over hyperfields, which gives a new approach to construct matroids over hyperfields. A recurring theme in our work is that various tropical constructions can be extended beyond tropicalization with new formulations and proof methods.
Keywords
Cite
@article{arxiv.2005.01787,
title = {Oriented Matroids from Triangulations of Products of Simplices},
author = {Marcel Celaya and Georg Loho and Chi Ho Yuen},
journal= {arXiv preprint arXiv:2005.01787},
year = {2020}
}
Comments
v2: The original submission was split in two parts. This is an improved version of the first part. 43 pages, 18 Figures; v1: 51 pages, 15 Figures