A Tverberg Type Theorem for Matroids

Imre Bárány (), Gil Kalai () and Roy Meshulam ()
Additional contact information
Imre Bárány: Hungarian Academy of Sciences, Rényi Institute
Gil Kalai: Hebrew University, Einstein Institute of Mathematics
Roy Meshulam: Technion, Department of Mathematics

A chapter in A Journey Through Discrete Mathematics, 2017, pp 115-121 from Springer

Abstract: 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 ) ≠ ∅ $$\bigcap _{i=1}^{t}f(\sigma _{i})\neq \emptyset$$ .

Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-44479-6_5

Ordering information: This item can be ordered from
http://www.springer.com/9783319444796

DOI: 10.1007/978-3-319-44479-6_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().