2020/05/04 by Marcel Celaya, Georg Loho, Celaya, Marcel +3
Computer Science · Mathematics · Engineering · #Polynomial and algebraic computation #Commutative Algebra and Its Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2005.01787
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.