Abstract

HERNANDEZ-FLORES, Alan  and  MONTOYA-VEGA, Gabriel. Alexander-Conway and bracket polynomials of a family of pretzel links. Integración - UIS [online]. 2025, vol.43, n.2, pp.27-43.  Epub Oct 18, 2025. ISSN 0120-419X.  https://doi.org/10.18273/revint.v43n2-2025003.

Polynomial invariants constitute a dynamic and essential area of study in knot theory. From the pioneer Alexander polynomial, the revolutionary Jones polynomial, to the collectively discovered HOMFLYPT polynomial (just to mention a few), these algebraic expressions have been central to the understanding of knots and links. Even more with the recent introduction of Khovanov homology that has sparked significant interest in the categorification of these polynomials, offering deeper insights into their topological and algebraic properties. In this work, we revisit two prominent polynomial invariants-the Alexander-Conway and the Kauffman bracket-and focus specifically on the polynomials associated with the family of three-strand pretzel links P (1, 1, n).

Keywords : Knots and links; pretzel links; Alexander-Conway polynomial; Kauffman bracket polynomial.

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