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arXiv · 2502.03673

Turán densities for matroid basis hypergraphs

Jorn van der Pol·Zach Walsh·Michael C. Wigal
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Abstract

Let $U$ be a uniform matroid. For all positive integers $n$ and $r$ with $n \ge r$, what is the maximum number of bases of an $n$-element, rank-$r$ matroid without $U$ as a minor? We show that this question arises by restricting the problem of determining the Turán number of a daisy hypergraph to the family of matroid basis hypergraphs. We then answer this question for several interesting choices of $U$.

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Jorn van der Pol, Zach Walsh, Michael C. Wigal. 2025-03-10. Turán densities for matroid basis hypergraphs. https://arxiv.org/abs/2502.03673

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