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Fractal classes of matroids

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journal contribution
posted on 2021-12-01, 19:36 authored by Dillon Mayhew, M Newman, Geoffrey WhittleGeoffrey Whittle
A minor-closed class of matroids is (strongly) fractal if the number of n-element matroids in the class is dominated by the number of n-element excluded minors. We conjecture that when K is an infinite field, the class of K-representable matroids is strongly fractal. We prove that the class of sparse paving matroids with at most k circuit-hyperplanes is a strongly fractal class when k is at least three. The minor-closure of the class of spikes with at most k circuit-hyperplanes (with k≥5) satisfies a strictly weaker condition: the number of 2t-element matroids in the class is dominated by the number of 2t-element excluded minors. However, there are only finitely many excluded minors with ground sets of odd size.

History

Preferred citation

Mayhew, D., Newman, M. & Whittle, G. (2021). Fractal classes of matroids. Advances in Applied Mathematics, 126, 101995-101995. https://doi.org/10.1016/j.aam.2019.101995

Journal title

Advances in Applied Mathematics

Volume

126

Publication date

2021-05-01

Pagination

101995-101995

Publisher

Elsevier BV

Publication status

Published

ISSN

0196-8858

eISSN

1090-2074

Article number

101995

Language

en