Discrete Mathematics & Theoretical Computer Science, Vol 5 (2002)

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DMTCS vol 5 no 1 (2002), pp. 181-190

Discrete Mathematics & Theoretical Computer Science


Volume 5 n° 1 (2002), pp. 181-190

author:W.M.B. Dukes
title:On a Unimodality Conjecture in Matroid Theory
keywords:Matroid Theory, Unimodality Conjecture, Rank-2 matroids, Rank-3 matroids
abstract:A certain unimodal conjecture in matroid theory states 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-2 matroids into the class of loopless rank-3 matroids. Similar inequalities are proven for the number of non-isomorphic loopless matroids, loopless matroids and matroids.

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reference: W.M.B. Dukes (2002), On a Unimodality Conjecture in Matroid Theory, Discrete Mathematics and Theoretical Computer Science 5, pp. 181-190
bibtex:For a corresponding BibTeX entry, please consider our BibTeX-file.
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