The Borsuk-Ulam theorem and bisection of necklaces

Noga Alon, Douglas B. West

Research output: Contribution to journalArticle

44 Scopus citations

Abstract

The Borsuk-Ulam theorem of topology is applied to a problem in discrete mathematics. A bisection of a necklace with k colors of beads is a collection of intervals whose union captures half the beads of each color. Every necklace with k colors has a bisection formed by at most k cuts. Higherdimensional generalizations are considered.

Original languageEnglish (US)
Pages (from-to)623-628
Number of pages6
JournalProceedings of the American Mathematical Society
Volume98
Issue number4
DOIs
StatePublished - Dec 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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