Block partitions: an extended view.

Given a sequence S=(s1,…,sm)∈[0,1]m<inline-graphic></inline-graphic>, a block B of S is a subsequence B=(si,si+1,…,sj)<inline-graphic></inline-graphic>. 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, …,<inline-graphic></inline-graphic>Bn with |bi-bj|≤1<inline-graphic></inline-graphic> for every i, j. In this paper, we consider a generalization of the problem in higher dimensions. [ABSTRACT FROM AUTHOR]