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.
Original language | English |
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Article number | 47 |
Journal | Selecta Mathematica, New Series |
Volume | 30 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2024 |
Keywords
- 05E45
- 12K99
- 14T15
- 52B40
- 52C40