On partitions of a rectangle into rectangles with restricted number of cross sections

Abstract

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. © Springer-Verlag Berlin Heidelberg 2006.