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Consider partitions of a rectangle into rectangles with restricted number of cross sections. The problem has an information theoretic flavor (in the spirit of [3]): richness of two dimensional pictures under 1–dimensional restrictions of from local information to global information.We present two approaches to upper bound the cardinality of such partitions: a combinatorial recursion and harmonic analysis.

On Partitions of a Rectangle into Rectangles with Restricted Number of Cross Sections