Block Partitions of Sequences
Combinatorics
2014-06-24 v4
Abstract
Given a sequence A=(a1,...,an) of real numbers, a block B of the A is either a set B={ai,...,aj} where i<=j or the empty set. The size b of a block B is the sum of its elements. We show that when 0<=ai<=1 and k is a positive integer, there is a partition of A into k blocks B1,...,Bk with |bi-bj|<=1 for every i, j. We extend this result in many directions.
Cite
@article{arxiv.1308.2452,
title = {Block Partitions of Sequences},
author = {Imre Bárány and Victor S. Grinberg},
journal= {arXiv preprint arXiv:1308.2452},
year = {2014}
}
Comments
9 pages