Euclideaness and final polynomials in oriented matroid theory

Abstract

This paper deals with a geometric construction of algebraic non-realizability proofs for certain oriented matroids. As main result we obtain an algorithm which generates a (bi-quadratic) final polynomial [3], [5] for any non-euclidean oriented matroid. Here we apply the results of Edmonds, Fukuda and Mandel [6], [7] concerning non-degenerate cycling of linear programs in non-euclidean oriented matroids.

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Richter-Gebert, J. Euclideaness and final polynomials in oriented matroid theory. Combinatorica 13, 259–268 (1993). https://doi.org/10.1007/BF01202352

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AMS subject classification code (1991)

  • 05 B 35
  • 51 A 25