## Projective Orientations of Matroids

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

ABSTRACT

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