Ordered matroids and regular independence systems

J.Orestes Cerdeira, Paulo Barcia
1996 Discrete Mathematics  
We consider a class of matroids which we call ordered matroids. We show that these are the matroids of regular independence systems. (If E is a finite ordered set, a regular independence system on E is an independence system (E, F) with the following property: if A E 9 and a E A, then (A -{a}) U {e} E 9 for all e E E-A such that e <a.) We give a necessary and sufficient condition for a regular independence system to be a matroid. This condition is checkable with a linear number of calls to an
more » ... dependence oracle. With this condition we rediscover some known results relating regular O/l polytopes and matroids.
doi:10.1016/0012-365x(94)00352-j fatcat:t5gu3ytes5bvxnscyns6ebmuum