Oriented matroids from triangulations of products of simplices

Abstract: Classically, there is a rich theory in algebraic combinatorics surrounding the various objects associated with a generic real matrix. Examples include regular triangulations of the product of two simplices, coherent matching fields, and realizable oriented matroids. In this talk, we will extend the theory by skipping the matrix and starting with an arbitrary triangulation of the product of two simplices instead. In particular, we show that every polyhedral matching field induces oriented matroids. The oriented matroid is composed of compatible chirotopes on the cells in a matroid subdivision of the hypersimplex. Furthermore, we give a corresponding topological construction using Viro’s patchworking. This allows to derive a representation of the oriented matroid as a pseudosphere arrangement from a fine mixed subdivision. This is joint work with Marcel Celaya and Chi-Ho Yuen.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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