Splitting necklaces

Research output: Contribution to journalArticle

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Abstract

Let N be an opened necklace with kai beads of color i, 1 ≤ i ≤ t. We show that it is possible to cut N in (k - 1) · t places and partition the resulting intervals into k collections, each containing precisely ai beads of color i, 1 ≤ i ≤ t. This result is best possible and solves a problem of Goldberg and West. Its proof is topological and uses a generalization, due to Bárány, Shlosman and Szücs, of the Borsuk-Ulam theorem. By similar methods we obtain a generalization of a theorem of Hobby and Rice on L1-approximation.

Original languageEnglish (US)
Pages (from-to)247-253
Number of pages7
JournalAdvances in Mathematics
Volume63
Issue number3
DOIs
StatePublished - Mar 1987

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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