The rectangle complexity of functions on two-dimensional lattices

Let X be a non-empty set. Let f:Z2X. All vectors which occur have integer coefficients, and for =(a1,a2), =(b1,b2) we write or 0. A -block is a set of the form B(){Z2| 0 such that the -complexity of f does not exceed b1b2. In this paper, we prove the statement for b=(n,2) where n is any positive integer.