Doubly exponentially many ingleton matroids

Peter Nelson; Jorn van der Pol

doi:10.1137/17M1160094

Doubly exponentially many ingleton matroids

Peter Nelson, Jorn van der Pol

Mathematics and Computer Science

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

72 Downloads (Pure)

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 nonrepresentable.

Original language	English
Pages (from-to)	1145-1153
Number of pages	9
Journal	SIAM Journal on Discrete Mathematics
Volume	32
Issue number	2
DOIs	https://doi.org/10.1137/17M1160094
Publication status	Published - 1 Jan 2018

Keywords

Enumeration
Matroid
Representable

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10.1137/17M1160094

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Doubly exponentially many ingleton matroids

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