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.

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Academic Press
European Journal of Combinatorics
Quantum Information Processing
Quantum Computing and Advanced System Research

Noga, A, Newman, I, Tardos, G, Shen, A, & Vereshchagin, N.K. (2007). Partitioning multi-dimensional sets in a small number of ``uniform'' parts. European Journal of Combinatorics, 28, 134–144.