Abstract
Let N be an opened necklace with ka i 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 a i 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 L 1 -approximation.
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