# 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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