Mayhew, D. orcid.org/0000-0003-4086-0980, Newman, M. and Whittle, G. (2021) Fractal classes of matroids. Advances in Applied Mathematics, 126. 101995. ISSN 0196-8858
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020, Elsevier Inc. This is an author produced version of an article accepted for publication in Advances in Applied Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Jan 2024 15:08 |
Last Modified: | 28 Jan 2024 01:21 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aam.2019.101995 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:208140 |