Block partitions: an extended view

I. Bárány, E. Csóka, Gy. Károlyi +1

Given a sequence $S=(s_1,\dots ,s_m)\in [0,1{]}^m$, a block $B$ of $S$ is a subsequence $B=(s_i,s_{i+1},\dots ,s_j)$. The size $b$ of a block $B$ is the sum of its elements. It is pr…