A generalisation of uniform matroids

Drummond, George

doi:10.1016/j.aam.2021.102248

Cited by 2 publications

(1 citation statement)

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“…For split matroids, Joswig and Schröter [10, Question A] identified five forbidden minors, and Cameron and Mayhew [3] later verified that the list is complete. It is worth mentioning that U 0,ℓ ⊕ U k,k -minor-free matroids were studied for positive integers k and ℓ in general [5], while [18] gave excluded-minor characterizations for the class of so-called nearly-uniform and nearly-paving matroids.…”

Section: Introductionmentioning

confidence: 99%

Hypergraph characterization of split matroids

Bérczi¹,

Király²,

Schwarcz³

et al. 2022

Preprint

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We provide a combinatorial study of split matroids, a class that was motivated by the study of matroid polytopes from a tropical geometry point of view. A nice feature of split matroids is that they generalize paving matroids, while being closed under duality and taking minors. Furthermore, these matroids proved to be useful in giving exact asymptotic bounds for the dimension of the Dressian, and also implied new results on the rays of the tropical Grassmannians.In the present paper, we introduce the notion of elementary split matroids, a subclass of split matroids that contains all connected split matroids. We give a hypergraph characterization of elementary split matroids in terms of independent sets, and show that the proposed class is closed not only under duality and taking minors but also truncation. We further show that, in contrast to split matroids, the proposed class can be characterized by a single forbidden minor. As an application, we provide a complete list of binary split matroids.

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Section: Introductionmentioning

confidence: 99%