Alexander-Conway and Bracket Polynomials of Pretzel Links $\boldsymbol{P(1,1,n)}$

Abstract: Polynomial invariants constitute a dynamic and essential area of study in the mathematical theory of knots. 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. The introduction of Khovanov homology 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 polynomials, and focus specifically on the polynomials associated with the family of three strand pretzel links $P(1,1,n)$.