Oriented matroids from triangulations of products of simplices

Marcel Celaya, Georg Loho*, Chi Ho Yuen

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摘要

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.

原文English
文章編號47
期刊Selecta Mathematica, New Series
30
發行號3
DOIs
出版狀態Published - 7月 2024

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