Every non-Euclidean oriented matroid admits a biquadratic final polynomial

Abstract

Richter-Gebert proved that every non-Euclidean uniform oriented matroid admits a biquadratic final polynomial. We extend this result to the non-uniform case.

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Correspondence to Komei Fukuda.

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Research supported by the Swiss National Science Foundation Project 200021-105202, “Polytopes, Matroids and Polynomial Systems”.

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Fukuda, K., Moriyama, S., Nakayama, H. et al. Every non-Euclidean oriented matroid admits a biquadratic final polynomial. Combinatorica 29, 691–698 (2009). https://doi.org/10.1007/s00493-009-2255-2

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Mathematics Subject Classification (2000)

  • 52C35
  • 52C40