Some formulas for numbers of line segments and lines in a rectangular grid

2011/08/04 by Pentti Haukkanen, Haukkanen, Pentti, Jorma K. Merikoski +1
Mathematics · #05A99 #11B37 #11P21 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A99 #msc:11B37 #msc:11P21

paper · pdf · doi:10.48550/arxiv.1108.1041

arxiv created 2011/08/04 · arxiv updated 2011/08/05

Abstract

We present a formula for the number of line segments connecting q+1 points of an n₁ x...x n_k rectangular grid. As corollaries, we obtain formulas for the number of lines through at least q points and, respectively, through exactly q points of the grid. The well-known case k=2 is so generalized. We also present recursive formulas for these numbers assuming k=2, n₁=n₂. The well-known case q=2 is so generalized.

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