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Every non-Euclidean oriented matroid admits a biquadratic final polynomial

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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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Authors and Affiliations

  1. Institute for Operations Research, ETH Zentrum, Zurich, CH-8092, Switzerland

    Komei Fukuda

  2. Institute of Theoretical Computer Science, ETH Zentrum, Zurich, CH-8092, Switzerland

    Komei Fukuda

  3. Institute for Nano Quantum Information Electronics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Sonoko Moriyama

  4. Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

    Hiroki Nakayama

  5. Technische Universität München Zentrum Mathematik (M10) Lehrstuhl für Geometrie und Visualisierung, Boltzmannstr. 3, Garching bei München, D-85748, Germany

    Jürgen Richter-Gebert

Authors
  1. Komei Fukuda
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  2. Sonoko Moriyama
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  3. Hiroki Nakayama
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  4. Jürgen Richter-Gebert
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Corresponding author

Correspondence to Komei Fukuda.

Additional information

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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  • DOI: https://doi.org/10.1007/s00493-009-2255-2

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