Title

Bounding the number of bases of a matroid

Document Type

Article

Publication Date

6-1-1995

Abstract

Let b(M) and c(M), respectively, be the number of bases and circuits of a matroid M. For any given minor closed classℳ of matroids, the following two questions, are investigated in this paper. (1) When is there a polynomial function p(x) such that b(M)≤p(c(m)|E(M)|) for every matroid M inℳ? (2) When is there a polynomial function p(x) such that b(M)≤p(|E(M)|) for every matroid M inℳ? Let us denote by MMn the direct sum of n copies of U1,2. We prove that the answer to the first question is affirmative if and only if some MMn is not inℳ. Furthermore, if all the members ofℳ are representable over a fixed finite field, then we prove that the answer to the second question is affirmative if and only if, also, some MMn is not inℳ. © 1995 Akadémiai Kiadó.

Publication Source (Journal or Book title)

Combinatorica

First Page

159

Last Page

165

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