Computing Alexander polynomials for arborescent links

TL;DR

This paper introduces an efficient recursive method to compute Alexander polynomials for arborescent links, including explicit formulas for pretzel links, enhancing computational tools in knot theory.

Contribution

The paper develops a novel recursive approach to compute Alexander polynomials for arborescent links, with explicit formulas for pretzel links, improving computational efficiency.

Findings

Derived explicit formulas for pretzel links' Alexander polynomials.

Presented a recursive method for arborescent links.

Enhanced computational techniques in knot theory.

Abstract

For arborescent links, we present an efficient method of computing their Alexander polynomials. Applying this method, we express the Alexander polynomials of Montesinos links in terms of certain functions associated to rational tangles which can be computed recursively. Specifically, we deduce explicit closed formulas for all pretzel links.