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Excluded Minors for Matroids Satisfying Kinser’s Inequalities

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Abstract

Kinser developed a hierarchy of inequalities for subspaces. These inequalities can be applied to the rank function of a matroid, and a matroid which is representable must satisfy each one of them. We provide results on the matroids which satisfy each inequality and the structure of the hierarchy of such matroids. We strengthen a result by Mayhew, Newman, and Whittle by showing that for every real-representable matroid \(M\) and every layer of the hierarchy, there is an excluded minor for that layer of the hierarchy that contains \(M\) as a minor.

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Acknowledgments

We would like to thank the referee of this paper for their helpful comments.

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Author notes

  1. Amanda Cameron

    Present address: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS, UK

Authors and Affiliations

  1. School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand

    Amanda Cameron & Dillon Mayhew

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  1. Amanda Cameron
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  2. Dillon Mayhew
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Correspondence to Amanda Cameron.

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Cameron, A., Mayhew, D. Excluded Minors for Matroids Satisfying Kinser’s Inequalities. Graphs and Combinatorics 32, 31–47 (2016). https://doi.org/10.1007/s00373-015-1555-0

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  • DOI: https://doi.org/10.1007/s00373-015-1555-0

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