Block partitions: an extended view

Given a sequence S = ( s 1 , … , s m ) ∈ [ 0 , 1 ] m , a block B of S is a subsequence B = ( s i , s i + 1 , … , 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 , … , B n with | b i - b j...

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Bibliographic Details
Published in:Acta mathematica Hungarica 2018-06, Vol.155 (1), p.36-46
Main Authors: Bárány, I., Csóka, E., Károlyi, Gy, Tóth, G.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Partitions (mathematics)
Citations: Items that this one cites
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Summary:Given a sequence S = ( s 1 , … , s m ) ∈ [ 0 , 1 ] m , a block B of S is a subsequence B = ( s i , s i + 1 , … , 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 , … , B n with | b i - b j | ≤ 1 for every i , j . In this paper, we consider a generalization of the problem in higher dimensions.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-018-0802-2