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A Tverberg Type Theorem for Matroids

  • Imre Bárány
  • Gil Kalai
  • Roy Meshulam
Chapter

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 σ1, , σ t M such that \(\bigcap _{i=1}^{t}f(\sigma _{i})\neq \emptyset\).

Notes

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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Copyright information

© Springer International publishing AG 2017

Authors and Affiliations

  1. 1.Rényi InstituteHungarian Academy of SciencesBudapestHungary
  2. 2.Department of MathematicsUniversity College LondonLondonUK
  3. 3.Einstein Institute of MathematicsHebrew UniversityJerusalemIsrael
  4. 4.Department of MathematicsTechnionHaifaIsrael

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