LCP DEGREE THEORY AND ORIENTED MATROIDS

It is shown that the degree of a square-oriented matroid M can be defined in terms of the number of solutions to the oriented matroid complementarity problem defined by a point extension of M, and that this definition is independent of the point extension. If M is represented by a matrix [I, M], then this degree is the same as the degree of the LCP mapping defined by M. The average value of the degree is determined. A new characterization of P-matrices in terms of degree theory is given. A negative result concerning Q-matrices defining maps of degree zero is presented.