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 language||English (US)|
|Number of pages||7|
|Journal||Advances in Mathematics|
|State||Published - Mar 1987|
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