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arXiv · 1710.01924

Doubly exponentially many Ingleton matroids

Peter Nelson·Jorn van der Pol
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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 $[n]$ is doubly exponential in $n$; it follows that almost all Ingleton matroids are non-representable.

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Peter Nelson, Jorn van der Pol. 2017-10-05. Doubly exponentially many Ingleton matroids. https://arxiv.org/abs/1710.01924

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