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A Tverberg Type Theorem for Matroids

In: A Journey Through Discrete Mathematics

Author

Listed:
  • Imre Bárány

    (Hungarian Academy of Sciences, Rényi Institute
    University College London, Department of Mathematics)

  • Gil Kalai

    (Hebrew University, Einstein Institute of Mathematics)

  • Roy Meshulam

    (Technion, Department of Mathematics)

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 ℝ d $$\mathbb{R}^{d}$$ there exist t ≥ b ( M ) ∕ 4 $$t \geq \sqrt{b(M)}/4$$ disjoint independent sets σ 1, …, σ t ∈ M such that ⋂ i = 1 t f ( σ i ) ≠ ∅ $$\bigcap _{i=1}^{t}f(\sigma _{i})\neq \emptyset$$ .

Suggested Citation

  • Imre Bárány & Gil Kalai & Roy Meshulam, 2017. "A Tverberg Type Theorem for Matroids," Springer Books, in: Martin Loebl & Jaroslav Nešetřil & Robin Thomas (ed.), A Journey Through Discrete Mathematics, pages 115-121, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-44479-6_5
    DOI: 10.1007/978-3-319-44479-6_5
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