2017/06/18 by Bárány, I., Csóka, E., Károlyi, Gy. +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1706.06095
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, … , Bn with |bi - bj| ≤ 1 for every i, j. In this paper, we consider a generalization of the problem in higher dimensions.