%0 Journal Article %@ 1588-2632 %A Barany, I %A Csoka, E %A Karolyi, G %A Toth, G %D 2018 %F discovery:1560883 %I SPRINGER %J Acta Mathematica Hungarica %K sequence, block partition, transversal %N 1 %P 36-46 %T Block partitions: an extended view %U https://discovery.ucl.ac.uk/id/eprint/1560883/ %V 155 %X 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. %Z This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.