Enumerative combinatorics
Journal of Computer and System Sciences
Fundamentals of Artificial Neural Networks
Fundamentals of Artificial Neural Networks
Enumeration of Threshold Functions of Eight Variables
IEEE Transactions on Computers
Enumeration of linear threshold functions from the lattice of hyperplane intersections
IEEE Transactions on Neural Networks
On encoding and enumerating threshold functions
IEEE Transactions on Neural Networks
Asymptotics of the number of threshold functions on a two-dimensional rectangular grid
Discrete Applied Mathematics
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A two-dimensional threshold function of $k$-valued logic can be viewed as a coloring of the points of a $k\times k$ 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.