%K sequence, block partition, transversal %V 155 %A I Barany %A E Csoka %A G Karolyi %A G Toth %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. %J Acta Mathematica Hungarica %N 1 %L discovery1560883 %I SPRINGER %D 2018 %O This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. %T Block partitions: an extended view %P 36-46