Toward a Connection between the Oriented Matroid Theory and Supersymmetry

Abstract

We considered the possibility that the oriented matroid theory is connected with supersymmetry via the Grassmann-Plucker relations. The main reason for this, is that such relations arise in both in the chirotopes definition of an oriented matroid, and in maximally supersymmetric solutions of eleven- and ten-dimensional supergravity theories. Taking this observation as a motivation, and using the concept of a phirotope, we propose a mechanism to implement supersymmetry in the context of the oriented matroid theory.