2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/178053We claim that $M$(atroid) theory may provide a mathematical framework for an underlying description of $M$-theory. Duality is the key symmetry which motivates our proposal. The definition of an oriented matroid in terms of the Farkas property plays a central role in our formalism. We outline how this definition may be carried over $M$-theory. As a consequence of our analysis we find a new type of action for extended systems which combines dually the $p$-brane and its dual $p^{\perp}$-brane.12 pages, Latex; some improvements introduced, typos correctedHigh Energy Physics - Theorytext