The Weight System of the Multivariable Alexander Polynomial
Jana Archibald
TL;DR
This paper derives a determinant-based formula for the weight system of the multivariable Alexander polynomial, demonstrating its adherence to known relations and similarities with the single-variable case.
Contribution
It introduces a new determinant formula for the multivariable Alexander polynomial's weight system and explores its relation to existing polynomial invariants.
Findings
The weight system obeys known relations for knot invariants.
It satisfies similar relations as the single-variable Alexander polynomial.
The formula provides a new computational approach.
Abstract
We derive a formula for the weight system of the multivariable Alexander polynomial using determinants, show that it obeys known relations, and satisfies some of the same relations as the single variable polynomial.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Algebraic structures and combinatorial models