Doubly exponentially many Ingleton matroids
Combinatorics
2017-10-06 v1
Abstract
A matroid is Ingleton if all quadruples of subsets of its ground set satisfy Ingleton's inequality. In particular, representable matroids are Ingleton. We show that the number of Ingleton matroids on ground set is doubly exponential in ; it follows that almost all Ingleton matroids are non-representable.
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Cite
@article{arxiv.1710.01924,
title = {Doubly exponentially many Ingleton matroids},
author = {Peter Nelson and Jorn van der Pol},
journal= {arXiv preprint arXiv:1710.01924},
year = {2017}
}
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11 pages