On Chebyshev Polynomials and Torus Knots
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...
Збережено в:
| Дата: | 2010 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Відділення фізики і астрономії НАН України
2010
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| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/13295 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 with the Alexander polynomials for the class T(s, 2) of torus knots, s being an odd integer, and used for finding the corresponding skein relation. Then, we develop this procedure in order to obtain, with the help of q, p - numbers, the generalized two-variable Alexander polynomials and to prove their direct connection with the HOMFLY polynomials and the skein relation of the latter. |
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