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

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## Abstract

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 |
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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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