Asymptotics for numbers of line segments and lines in a square grid
Number Theory
2012-05-16 v1 Information Theory
Combinatorics
math.IT
Abstract
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 present asymptotic formulas for the number of lines through at least q points and, respectively, through exactly q points of the grid. The well-known case q=2 is so generalized.
Cite
@article{arxiv.1110.6864,
title = {Asymptotics for numbers of line segments and lines in a square grid},
author = {Pentti Haukkanen and Jorma K. Merikoski},
journal= {arXiv preprint arXiv:1110.6864},
year = {2012}
}