Enumerating Low Rank Matroids and their Asymptotic Probability of Occurrence

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
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 13 Jun 2018 13:07
Last Modified: 17 Jul 2018 13:09
URI: http://dair.dias.ie/id/eprint/439

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