On the number of two-dimensional threshold functions

Details On the number of two-dimensional threshold functions On the number of two-dimensional threshold functions

2006-02-23

arxiv.org/abs/math/0602511v4

SIAM J. Discrete Math. 24(4), pp. 1617-1631 (2010)

Mathematics

Combinatorics

17 pages, 2 figures

Scientific paper

10.1137/090750184

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.

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