Modular elimination in matroids and oriented matroids

Emanuele Delucchi

Published 2010-02-11, updated 2016-08-22Version 2

We introduce a new axiomatization of matroid theory that requires the elimination property only among modular pairs of circuits, and we present a cryptomorphic phrasing thereof in terms of Crapo's axioms for flats. This new point of view leads to a corresponding strengthening of the circuit axioms for oriented matroids.