%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