Dilworth truncations and k-induced matroids

✍ Scribed by Randell A. Stevenson

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 440 KB
• Volume: 105
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(92)90142-3

✦ Synopsis

E+ 2', the subsets I of E such that 11'1 c r&9(1'))

k for all non-empty subsets I' of I are the independent sets of a matroid on E. This matroid is said to be k-induced on Q by 4. The aim of this paper is to prove that if k and n are nonnegative integers and M is a matroid

on the nth Dilworth truncation of Q. As a consequence, if M is l-induced on a free matroid, then M is O-induced on a graphic matroid Another consequence, a generalization of a well-known result of Mason and Brylawski, is that for any integer k, if Q is representable over a field F and M is k-induced on Q, then M is representable over an extension of F. The converses of these statements do not hold in general.