Discrete & Computational Geometry

, Volume 49, Issue 2, pp 287–295

New Examples of Oriented Matroids with Disconnected Realization Spaces

Article

DOI: 10.1007/s00454-012-9456-y

Cite this article as:
Tsukamoto, Y. Discrete Comput Geom (2013) 49: 287. doi:10.1007/s00454-012-9456-y

Abstract

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

Keywords

Oriented matroids Realization space 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Human CoexistenceKyoto UniversityKyotoJapan