A polynomial pair invariant of alternating knots and links
Geometric Topology
2025-05-27 v3
Abstract
We introduce an invariant of alternating knots and links (called here WRP), namely a pair of integer polynomials associated with their two checkerboard planar graphs from their minimal diagram. We prove that the invariant is well-defined and give its values obtained from calculations for some knots in the tables. This invariant is strong enough to distinguish all knots in the tables with up to 10 crossings (including their mirror images). We compare the strength of the new invariant with classical invariants, including the three-variable Kauffman bracket.
Keywords
Cite
@article{arxiv.2307.08516,
title = {A polynomial pair invariant of alternating knots and links},
author = {Michal Jablonowski},
journal= {arXiv preprint arXiv:2307.08516},
year = {2025}
}