We define slopes in the flat torus as the set of equivalence classes of the solutions of linear equations in $\mathbb{R}^2$. The definition is equivalent to that of closed geodesics in the flat torus passing through the equivalence class of the point $(0,0)$. In this paper we derive formulas for counting the number of points in the intersection of multiple slopes in the flat torus.
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Burke, J. , Burke, M. , Pinheiro, L. and Richer, C. (2024). Methods for counting the intersections of slopes in the flat torus. Transactions on Combinatorics, 13(4), 305-317. doi: 10.22108/toc.2023.135546.2023
MLA
Burke, J. , , Burke, M. , , Pinheiro, L. , and Richer, C. . "Methods for counting the intersections of slopes in the flat torus", Transactions on Combinatorics, 13, 4, 2024, 305-317. doi: 10.22108/toc.2023.135546.2023
HARVARD
Burke, J., Burke, M., Pinheiro, L., Richer, C. (2024). 'Methods for counting the intersections of slopes in the flat torus', Transactions on Combinatorics, 13(4), pp. 305-317. doi: 10.22108/toc.2023.135546.2023
CHICAGO
J. Burke , M. Burke , L. Pinheiro and C. Richer, "Methods for counting the intersections of slopes in the flat torus," Transactions on Combinatorics, 13 4 (2024): 305-317, doi: 10.22108/toc.2023.135546.2023
VANCOUVER
Burke, J., Burke, M., Pinheiro, L., Richer, C. Methods for counting the intersections of slopes in the flat torus. Transactions on Combinatorics, 2024; 13(4): 305-317. doi: 10.22108/toc.2023.135546.2023