Block partitions of sequences

Bárány, Imre and Grinberg, V.S. (2015) Block partitions of sequences. ISRAEL JOURNAL OF MATHEMATICS, 206 (1). pp. 155-164. ISSN 0021-2172

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Abstract

Given a sequence A = (a1, …, an) of real numbers, a block B of A is either a set B = {ai, ai+1, …, aj} where i ≤ j or the empty set. The size b of a block B is the sum of its elements. We show that when each ai ∈ [0, 1] and k is a positive integer, there is a partition of A into k blocks B1, …, Bk with |bi−bj| ≤ 1 for every i, j. We extend this result in several directions. © 2015, Hebrew University of Jerusalem.

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