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arXiv · 2005.01787

Oriented Matroids from Triangulations of Products of Simplices

Marcel Celaya·Georg Loho·Chi Ho Yuen
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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.

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Marcel Celaya, Georg Loho, Chi Ho Yuen. 2020-05-04. Oriented Matroids from Triangulations of Products of Simplices. https://arxiv.org/abs/2005.01787

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