2020/10/22 by Marcel Celaya, Georg Loho, Celaya, Marcel +3
Computer Science · Mathematics · #14T15 #52C30 #52C40 (Primary) 05E45 #57N60 #57Q99 (Secondary) #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Formal Methods in Verification #Geometric Topology (math.GT) #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2010.12018
openalex publication_date 2020/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous work, we gave a construction of (not necessarily realizable) oriented matroids from a triangulation of a product of two simplices. In this follow-up paper, we use a variant of Viro's patchworking to derive a topological representation of the oriented matroid directly from the polyhedral structure of the triangulation, hence finding a combinatorial manifestation of patchworking besides tropical algebraic geometry. We achieve this by rephrasing the patchworking procedure as a controlled cell merging process, guided by the structure of tropical oriented matroids. A key insight is a new promising technique to show that the final cell complex is regular.