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.
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