A geometric hall-type theorem

Andreas F. Holmsen, Leonardo Martinez-Sandoval, Luis Montejano

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We introduce a geometric generalization of Hall’s marriage theorem. For any family F = {X1,..., Xm} of finite sets in ℝd, we give conditions under which it is possible to choose a point xi ∈ Xi for every 1 ≤ i ≤ m in such a way that the points {x1,..., xm} ⊂ ℝd are in general position. We give two proofs, one elementary proof requiring slightly stronger conditions, and one proof using topological techniques in the spirit of Aharoni and Haxell’s celebrated generalization of Hall’s theorem.

Original languageEnglish
Pages (from-to)503-511
Number of pages9
JournalProceedings of the American Mathematical Society
Volume144
Issue number2
DOIs
StatePublished - 1 Feb 2016
Externally publishedYes

Keywords

  • Hall’s theorem
  • Matroids
  • Points in general position
  • Topological combinatorics

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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