On the number of two-dimensional threshold functions
Combinatorics
2010-12-09 v4 Logic
Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.math/0602511,
title = {On the number of two-dimensional threshold functions},
author = {Max A. Alekseyev},
journal= {arXiv preprint arXiv:math/0602511},
year = {2010}
}
Comments
17 pages, 2 figures