Block partitions of sequences |
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Authors: | Email author" target="_blank">Imre?BárányEmail author Victor?S?Grinberg |
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Institution: | 1.Rényi Institute of Mathematics,Hungarian Academy of Sciences,Budapest,Hungary;2.Department of Mathematics,University College London,London,England;3.Pittsburgh,USA |
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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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