Abstract
Let b(M) denote the maximal number of disjoint bases in a matroid M. It is shown that if M is a matroid of rank d + 1, then for any continuous map f from the matroidal complex M into \(\mathbb{R}^{d}\) there exist \(t \geq \sqrt{b(M)}/4\) disjoint independent sets σ 1, …, σ t ∈ M such that \(\bigcap _{i=1}^{t}f(\sigma _{i})\neq \emptyset\).
In memory of Jirka Matousek
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Acknowledgements
Research of Imre Bárány was partially supported by ERC advanced grant 267165, and by Hungarian National grant K 83767. Research of Gil Kalai was supported by ERC advanced grant 320924. Research of Roy Meshulam is supported by ISF and GIF grants.
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Bárány, I., Kalai, G., Meshulam, R. (2017). A Tverberg Type Theorem for Matroids. In: Loebl, M., Nešetřil, J., Thomas, R. (eds) A Journey Through Discrete Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-44479-6_5
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