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Methods for counting the intersections of slopes in the flat torus | ||
| Transactions on Combinatorics | ||
| مقاله 2، دوره 13، شماره 4، اسفند 2024، صفحه 305-317 اصل مقاله (1.52 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2023.135546.2023 | ||
| نویسندگان | ||
| John Burke* ؛ Maitland Burke؛ Leonardo Pinheiro؛ Cameron Richer | ||
| Department of Mathematical Sciences, Rhode Island College, 600 Mt. Pleasant Ave. Providence, RI 02908 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| torus؛ intersection of curves؛ counting methods | ||
| مراجع | ||
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[1] M. Chas,The Goldman bracket and the intersection of curves on surfaces, Geometry, groups and dynamics, Contemp. Math., 639 (2015) 73–83. | ||
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