%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.