Asymptotics of the number of threshold functions on a two-dimensional rectangular grid

Authors:
Pentti Haukkanen;Jorma K. Merikoski
Affiliations:
-;-
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

Let m,n=2, m@?n. It is well-known that the number of (two-dimensional) threshold functions on an mxn rectangular grid is t(m,n)=6@p^2(mn)^2+O(m^2nlogn)+O(mn^2loglogn)=6@p^2(mn)^2+O(mn^2logm). We improve the error term by showing that t(m,n)=6@p^2(mn)^2+O(mn^2).