Matroid Theory and Supergravity

TL;DR

This paper explores the connections between matroid theory and supergravity, revealing a relation between the dual of the Fano matroid and D=11 supergravity, with potential implications for M-theory.

Contribution

It establishes a novel link between matroid duality and supergravity solutions, suggesting new interdisciplinary research directions.

Findings

Relation between dual Fano matroid and D=11 supergravity

Connection between matroid regularity and octonions

Speculation on applications to M-theory

Abstract

In this work, we consider matroid theory. After presenting three different (but equivalent) definitions of matroids, we mention some of the most important theorems of such theory. In particular, we note that every matroid has a dual matroid and that a matroid is regular if and only 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 Fano matroid and D = 11 supergravity. Possible applications to M-theory are speculated upon.