Block partitions: an extended view

Given a sequence \(S=(s_1,\dots,s_m) \in [0, 1]^m\), a block \(B\) of \(S\) is a subsequence \(B=(s_i,s_{i+1},\dots,s_j)\). The size \(b\) of a block \(B\) is the sum of its elements. It is proved in [1] that for each positive integer \(n\), there is a partition of \(S\) into \(n\) blocks \(B_1, \do...

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Bibliographic Details
Published in:arXiv.org 2017-06
Main Authors: Bárány, I, Csóka, E, Gy Károlyi, Tóth, G
Format: Article
Language:English
Subjects:
Partitions
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Summary:Given a sequence \(S=(s_1,\dots,s_m) \in [0, 1]^m\), a block \(B\) of \(S\) is a subsequence \(B=(s_i,s_{i+1},\dots,s_j)\). The size \(b\) of a block \(B\) is the sum of its elements. It is proved in [1] that for each positive integer \(n\), there is a partition of \(S\) into \(n\) blocks \(B_1, \dots , B_n\) with \(|b_i - b_j| \le 1\) for every \(i, j\). In this paper, we consider a generalization of the problem in higher dimensions.
ISSN:2331-8422