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

zbMATH Open1270.05007arXiv1108.1041MaRDI QIDQ4909709

Jorma K. Merikoski, Pentti Haukkanen

Publication date: 21 March 2013

Abstract: 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 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, n_1=n_2. The well-known case q=2 is so generalized.

Full work available at URL: https://arxiv.org/abs/1108.1041

zbMATH Keywords

lattice pointsrectangular gridrecursive formula

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Recurrences (11B37) Lattice points in specified regions (11P21)

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