On the Number of Two-Dimensional Threshold Functions

Max A. Alekseyev
2010 SIAM Journal on Discrete Mathematics  
A two-dimensional threshold function of k-valued logic can be viewed as coloring of the points of a k x k square lattice into two colors such that there exists a straight line separating points of different colors. For the number of such functions only asymptotic bounds are known. We give an exact formula for the number of two-dimensional threshold functions and derive more accurate asymptotics.
doi:10.1137/090750184 fatcat:6juziwmth5fw5obkjryehcgdqe