Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas lattice
In this paper, a connection is established between the Jones polynomial of generalized weaving knots of type W(3,n,m) and the Chebyshev polynomial of the first kind. Consequently, it is proved that the coefficients of the Jones polynomial of weaving knots are essentially the Whitney numbers of Lucas...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-04-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844024049764 |
| _version_ | 1797220534104096768 |
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| author | Mark E. AlSukaiti Nafaa Chbili |
| author_facet | Mark E. AlSukaiti Nafaa Chbili |
| author_sort | Mark E. AlSukaiti |
| collection | DOAJ |
| description | In this paper, a connection is established between the Jones polynomial of generalized weaving knots of type W(3,n,m) and the Chebyshev polynomial of the first kind. Consequently, it is proved that the coefficients of the Jones polynomial of weaving knots are essentially the Whitney numbers of Lucas lattices. Additionally, an explicit formula for the coefficients of the Alexander polynomial of weaving knots W(3,n) is introduced, and it is proven that these coefficients satisfy Fox's trapezoidal conjecture. |
| first_indexed | 2024-04-24T12:51:04Z |
| format | Article |
| id | doaj.art-5a976cfdd76a4355be23cb3bfd0363fe |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-04-24T12:51:04Z |
| publishDate | 2024-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-5a976cfdd76a4355be23cb3bfd0363fe2024-04-06T04:40:10ZengElsevierHeliyon2405-84402024-04-01107e28945Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas latticeMark E. AlSukaiti0Nafaa Chbili1Department of Mathematical Sciences, College of Science, United Arab Emirates University, 15551 Al Ain, United Arab EmiratesCorresponding author.; Department of Mathematical Sciences, College of Science, United Arab Emirates University, 15551 Al Ain, United Arab EmiratesIn this paper, a connection is established between the Jones polynomial of generalized weaving knots of type W(3,n,m) and the Chebyshev polynomial of the first kind. Consequently, it is proved that the coefficients of the Jones polynomial of weaving knots are essentially the Whitney numbers of Lucas lattices. Additionally, an explicit formula for the coefficients of the Alexander polynomial of weaving knots W(3,n) is introduced, and it is proven that these coefficients satisfy Fox's trapezoidal conjecture.http://www.sciencedirect.com/science/article/pii/S2405844024049764Weaving knotsKnot polynomialsWhitney numbersTrapezoidal conjecture |
| spellingShingle | Mark E. AlSukaiti Nafaa Chbili Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas lattice Heliyon Weaving knots Knot polynomials Whitney numbers Trapezoidal conjecture |
| title | Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas lattice |
| title_full | Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas lattice |
| title_fullStr | Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas lattice |
| title_full_unstemmed | Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas lattice |
| title_short | Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas lattice |
| title_sort | alexander and jones polynomials of weaving 3 braid links and whitney rank polynomials of lucas lattice |
| topic | Weaving knots Knot polynomials Whitney numbers Trapezoidal conjecture |
| url | http://www.sciencedirect.com/science/article/pii/S2405844024049764 |
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