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math.NT2011★ 3 cited
Asymptotics for numbers of line segments and lines in a square grid
Pentti Haukkanen, Jorma K. Merikoski
We present an asymptotic formula for the number of line segments connecting q+1 points of an nxn square grid, and a sharper formula, assuming the Riemann hypothesis. We also presen…
math.CO2011
Asymptotics of the number of threshold functions on a two-dimensional rectangular grid
Pentti Haukkanen, Jorma K. Merikoski
Let , . It is well-known that the number of (two-dimensional) threshold functions on an rectangular grid is {eqnarray*} t(m,n)=\frac{6}{π^2}(mn)^2+O(m…
math.CO2011★ 1 cited
Some formulas for numbers of line segments and lines in a rectangular grid
Pentti Haukkanen, Jorma K. Merikoski
We present a formula for the number of line segments connecting q+1 points of an n_1 x...x n_k rectangular grid. As corollaries, we obtain formulas for the number of lines through…