P. Koseleff

most citedChebyshev diagrams for rational knots

6 citations · 8 across the 5 of their papers we have counts for

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math.GT2009

The first rational Chebyshev knots

Pierre-Vincent Koseleff, Daniel Pecker, Fabrice Rouillier

A Chebyshev knot $C (a, b, c, ϕ)$ is a knot which has a parametrization of the form $x (t) = T_{a} (t); y (t) = T_{b} (t); z (t) = T_{c} (t + ϕ),$ where $a, b, c$ are integers, $T_{n} (t)$ is the…

math.GT2009

Chebyshev diagrams for two-bridge knots

Pierre-Vincent Koseleff, Daniel Pecker

We show that every two-bridge knot $K$ of crossing number $N$ admits a polynomial parametrization $x = T_{3} (t), y = T_{b} (t), z = C (t)$ where $T_{k} (t)$ are the Chebyshev polynomials and $…

math.GT2009

On Fibonacci Knots

Pierre-Vincent Koseleff, Daniel Pecker

We show that the Conway polynomials of Fibonacci links are Fibonacci polynomials modulo 2. We deduce that, when $ n \not\equiv 0 \Mod 4$ and $(n, j) \neq = (3, 3),$ the Fibonacci knot…

math.GT2009★ 6 cited

Chebyshev diagrams for rational knots

Pierre-Vincent Koseleff, Daniel Pecker

We show that every rational knot $K$ of crossing number $N$ admits a polynomial parametrization $x = T_{a} (t), y = T_{b} (t), z = C (t)$ where $T_{k} (t)$ are the Chebyshev polynomials, $a = 3$ …