On Chebyshev Polynomials and Torus Knots

• Date: 2010
• Main Authors: Gavrilik, A.M., Pavlyuk, A.M.
• Format: Article
• Language: English
• Published: Відділення фізики і астрономії НАН України 2010
• Subjects: Загальні питання теоретичної фізики
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/13295
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Chebyshev Polynomials and Torus Knots / A.M. Gavrilik, A.M. Pavlyuk // Укр. фіз. журн. — 2010. — Т. 55, № 1. — С. 129-134. — Бібліогр.: 21 назв. — англ.

In this work, we demonstrate that the q-numbers and their two-parameter generalization, the q,p -numbers, can be used to obtain some polynomial invariants for torus knots and links. First, we show that the q-numbers, which are closely connected with the Chebyshev polynomials, can also be related wit...