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Block partitions: an extended view

Barany, I; Csoka, E; Karolyi, G; Toth, G; (2018) Block partitions: an extended view. Acta Mathematica Hungarica , 155 (1) pp. 36-46. 10.1007/s10474-018-0802-2. Green open access

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Abstract

Given a sequence S=(s1,…,sm)∈[0,1]m , a block B of S is a subsequence B=(si,si+1,…,sj) . 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 B1, …, B n with |bi−bj|≤1 for every i, j. In this paper, we consider a generalization of the problem in higher dimensions.

Type: Article
Title: Block partitions: an extended view
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s10474-018-0802-2
Publisher version: http://doi.org/10.1007/s10474-018-0802-2
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: sequence, block partition, transversal
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1560883
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