Abstract
Given a sequence A = (a 1, …, a n ) of real numbers, a block B of A is either a set B = {a i , a i+1, …, a j } 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 a i ∈ [0, 1] and k is a positive integer, there is a partition of A into k blocks B 1, …, B k with |b i −b j | ≤ 1 for every i, j. We extend this result in several directions.
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Bárány, I., Grinberg, V.S. Block partitions of sequences. Isr. J. Math. 206, 155–164 (2015). https://doi.org/10.1007/s11856-014-1137-5
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DOI: https://doi.org/10.1007/s11856-014-1137-5