On a Unimodal Conjecture in Matroid Theory

Dukes, W.M.B. (2001) On a Unimodal Conjecture in Matroid Theory. (Preprint)

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A certain unimodal conjecture in matroid theory states that the number of rank-r matroids on a set of size n is unimodal in r and attains its maximum at r = ⌊n/2⌋. We show that this conjecture holds up to r = 3 by constructing a map from a class of rank-3 matroids. Similar inequalities are proven for the number of non-isomorphic loopless matroids, loopless matroids and matroids.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 13 Jun 2018 13:09
Last Modified: 14 Dec 2022 15:12
URI: https://dair.dias.ie/id/eprint/442

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