2023/07/17 by Michał Jabłonowski, Jablonowski, Michal · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2307.08516
openalex publication_date 2023/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.