Csóka Endre: Block partition in higher dimensions

Given a sequence S = (s_1, …, s_m) ∈ [0,1]^m, a block B of S is a
subsequence B=(s_i, s_{i+1}, …, s_j). The size b of a block B is the
sum of its elements. It is proved by Bárány that for each positive
integer n, there is a partition of S into n blocks B_1, …, B_n with
|b_i − b_j| ≤ 1 for every i, j. In this paper, we consider a
generalization of the problem in higher dimensions.

A part of the talk is joint work with Imre Bárány, Gyula Károlyi and Géza Tóth.