A polynomial parametrization of torus knots

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dc.creatorKoseleff, Pierre-Vincent
dc.creatorPecker, Daniel
dc.date2007-12-14
dc.date.accessioned2026-07-07T08:49:20Z
dc.date.available2026-07-07T08:49:20Z
dc.descriptionFor every odd integer $N$ we give an explicit construction of a polynomial curve $\cC(t) = (x(t), y (t))$, where $°x = 3$, $°y = N + 1 + 2\pent N4$ that has exactly $N$ crossing points $\cC(t_i)= \cC(s_i)$ whose parameters satisfy $s_1 < ... < s_{N} < t_1 < ... < t_{N}$. Our proof makes use of the theory of Stieltjes series and Padé approximants. This allows us an explicit polynomial parametrization of the torus knot $K_{2,N}$.
dc.identifierhttps://arxiv.org/abs/0712.2408
dc.identifierhttp://arxiv.org/abs/0712.2408
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144263
dc.subjectHistory and Overview
dc.titleA polynomial parametrization of torus knots
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