MATROID THEORY AND SUPERGRAVITY

In this work, we consider matroid theory. After presenting three diffe rent (but equivalent) definitions of matroids, we mention some of the most important theorems of such theory. In particular, we note that ev ery matroid has a dual matroid and that a matroid is regular if and on ly if it is binary and includes no Fano matroid or its dual. We show a connection between this last theorem and octonions which at the same time, as it is known, are related to the Englert's solution of D = 11 supergravity. Specifically, we find a relation between the dual of Fan o matroid and D = 11 supergravity. Possible applications to M-theory a re speculated upon.