On the number of two-dimensional threshold functions
Max A. Alekseyev · 2009
2-D threshold function f is a function defined on the integer interior of a rectangular area [0, m] × [0, n] on a plane and takes values from the set {0, 1} such that there is a straight line separating the pre-images f −1 (0) and f −1 (1). For the number of such functions only asymptotic bounds were known. We give an exact formula for the number of 2-D threshold Let m, n ∈ N be positive integers and K be a rectangular area on a plane bounded by the lines x = 0, x = m, y = 0, y = n with an integer interior K0, i.e., K def = [0, m] × [0, n] and