Oriented matroids from triangulations of products of simplices

Celaya, Marcel ORCID: https://orcid.org/0000-0003-3480-4835, Loho, Georg and Yuen, Chi Ho 2024. Oriented matroids from triangulations of products of simplices. Selecta Mathematica (New Series) 30 , 47. 10.1007/s00029-024-00938-2

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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.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Springer Verlag (Germany)
ISSN:	1022-1824
Date of First Compliant Deposit:	17 October 2023
Date of Acceptance:	1 September 2023
Last Modified:	30 Apr 2024 09:33
URI:	https://orca.cardiff.ac.uk/id/eprint/163264

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