2024
DOI: 10.1007/s00029-024-00938-2
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Oriented matroids from triangulations of products of simplices

Marcel Celaya,
Georg Loho,
Chi Ho Yuen

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 … Show more

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