Euclideaness and final polynomials in oriented matroid theory

Jürgen Richter-Gebert

doi:10.1007/BF01202352

Euclideaness and final polynomials in oriented matroid theory

Jürgen Richter-Gebert

Chair of Geometry and Visualization

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	259-268
Number of pages	10
Journal	Combinatorica
Volume	13
Issue number	3
DOIs	https://doi.org/10.1007/BF01202352
State	Published - Sep 1993

Keywords

AMS subject classification code (1991): 05B35, 51A25

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10.1007/BF01202352

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title = "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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N2 - 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.

AB - 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.

KW - AMS subject classification code (1991): 05B35, 51A25

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VL - 13

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JO - Combinatorica

JF - Combinatorica

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Euclideaness and final polynomials in oriented matroid theory

Abstract

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