A Topological Representation Theorem for Tropical Oriented Matroids: Part I
Silke Horn
TL;DR
This paper introduces a tropical analogue of the Topological Representation Theorem for tropical oriented matroids, extending classical matroid theory into tropical geometry.
Contribution
It provides the first topological representation theorem for tropical oriented matroids, bridging tropical geometry and topological combinatorics.
Findings
Established a topological representation for tropical oriented matroids
Extended classical matroid concepts into tropical geometry
Lays groundwork for further tropical combinatorial topology studies
Abstract
Tropical oriented matroids were defined by Ardila and Develin in 2007 in analogy to (classical) oriented matroids. In this paper we present one tropical analogue for the Topological Representation Theorem.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models