Partitioning multi-dimensional sets in a small number of ``uniform'' parts
Noga, A., Ilan Newman, Gábor Tardos, Alexander Shen, Nikolay Vereshchagin · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2007
In this paper we prove that every finite subset of ZxZ can be partitioned into a small number of subsets so that, in each part all vertical sections have aproximately the same size and all horyzontal sections have aproximately the same size. The generalization of this statement is used to give a combinatorial interpretation to every information inequality.