Oriented matroids from triangulations of products of simplices

Marcel Celaya, Georg Loho*, Chi Ho Yuen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number47
JournalSelecta Mathematica, New Series
Volume30
Issue number3
DOIs
StatePublished - Jul 2024

Keywords

  • 05E45
  • 12K99
  • 14T15
  • 52B40
  • 52C40

Fingerprint

Dive into the research topics of 'Oriented matroids from triangulations of products of simplices'. Together they form a unique fingerprint.

Cite this