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New examples of oriented matroids with disconnected realization spaces

2012/01/12 by Yasuyuki Tsukamoto, Tsukamoto, Yasuyuki
Computer Science · Mathematics · #52C40 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.CO #msc:52C40

paper · pdf · doi:10.48550/arxiv.1201.2560

8 pages, 3 figures

arxiv created 2012/01/12 · openalex publication_date 2012/01/12 · arxiv updated 2012/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct oriented matroids of rank 3 on 13 points whose realization spaces are disconnected. They are defined on smaller points than the known examples with this property. Moreover, we construct the one on 13 points whose realization space is a connected and non-irreducible semialgebraic variety.

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