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Ordered matroids and regular independence systems

✍ Scribed by J.Orestes Cerdeira; Paulo Barcia

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 419 KB
Volume: 154
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00352-j

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✦ Synopsis

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 independence oracle. With this condition we rediscover some known results relating regular O/l polytopes and matroids.

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