Oriented matroids from triangulations of products of simplices

• Marcel Celaya ^[1] ; Georg Loho ^[2] ; Chi Ho Yuen ^[3]
  1. [1] Cardiff University

     Cardiff University

     Castle, Reino Unido

     
  2. [2] University of Twente

     University of Twente

     Países Bajos

     
  3. [3] Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu City, Taiwan

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 3, 2024, págs. 1-32
• Idioma: inglés
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• Resumen

  • 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.