Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas lattice

Mark E. AlSukaiti, Nafaa Chbili

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article numbere28945
JournalHeliyon
Volume10
Issue number7
DOIs
Publication statusPublished - Apr 15 2024

Keywords

  • Knot polynomials
  • Trapezoidal conjecture
  • Weaving knots
  • Whitney numbers

ASJC Scopus subject areas

  • General

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