Dukes, W.M.B.
(2000)
*Enumerating Low Rank Matroids and their Asymptotic Probability of Occurrence.*
(Preprint)

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## Abstract

This paper shows the attractive enumerative relations between matroids of low rank. It differs from past work in that, rather than attempting to examine the numbers of non-isomorphic matroids as proposed by Crapo [4], it looks directly at the number of matroids and then extends to their non-isomorphic counterparts. We give the (heretofore unknown) numbers for matroids on at most eight elements. Furthermore, we consider a random collection of r-sets of an n-set and examine the probability that these satisfy the matroid basis exchange axioms. The asymptotic behavior of this probability shows interesting characteristics. The r = 2 case corresponds to a problem in random graphs.

Item Type: | Article |
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Divisions: | School of Theoretical Physics > Preprints |

Date Deposited: | 13 Jun 2018 13:07 |

Last Modified: | 14 Dec 2022 20:45 |

URI: | https://dair.dias.ie/id/eprint/439 |

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