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.
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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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