Modular elimination in matroids and oriented matroids
arXiv:1002.2357 · doi:10.1016/j.ejc.2010.10.013
Abstract
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.
arXiv comment6 pages; v2: text modified in order to better reflect the published version, references updated