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تسجيل مستخدم جديدThe first rational Chebyshev knots
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تأليف
Pierre-Vincent Koseleff
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A Chebyshev knot ${cal C}(a,b,c,phi)$ is a knot which has a parametrization of the form $ x(t)=T_a(t); y(t)=T_b(t) ; z(t)= T_c(t + phi), $ where $a,b,c$ are integers, $T_n(t)$ is the Chebyshev polynomial of degree $n$ and $phi in R.$ We show that any two-bridge knot is a Chebyshev knot with $a=3$ and also with $a=4$. For every $a,b,c$ integers ($a=3, 4$ and $a$, $b$ coprime), we describe an algorithm that gives all Chebyshev knots $cC(a,b,c,phi)$. We deduce a list of minimal Chebyshev representations of two-bridge knots with small crossing number.
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A Chebyshev knot is a knot which admits a parametrization of the form $ x(t)=T_a(t); y(t)=T_b(t) ; z(t)= T_c(t + phi), $ where $a,b,c$ are pairwise coprime, $T_n(t)$ is the Chebyshev polynomial of degree $n,$ and $phi in RR .$ Chebyshev knots are n
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