DIMACS TR: 93-02

Projective Orientations of Matroids

Authors: I. M. Gelfand, G. L. Rybnikov, and D. Stone


Let $\bold M$ be a matroid on a finite set. Let ${\Cal M}({\bold M})$ denote the set of oriented matroids whose underlying matroid is $\bold M$. We define an equivalence relation on ${\Cal M}({\bold M})$ in terms of ``reorientations'' of oriented matroids. The set of reorientation classes of oriented matroids on $\bold M$ is characterized in various combinatorial and algebraic ways. As part of this work we find two presentations of the inner Tutte group of $\bold M$ by generators and relations.

Paper available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1993/93-02.ps
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