2023/07/12 by Andreani Petrou, Petrou, Andreani, S. Hikami +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Physical sciences #Geometric and Algebraic Topology #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2307.05919
openalex publication_date 2023/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In an attempt to generalise knot matrix models for non-torus knots, which currently remains an open problem, we derived formulas for the Harer-Zagier transform of the HOMFLY-PT polynomial for some infinite families of twisted hyperbolic knots. Among them, we found a family of Pretzel knots for which the transform has a fully factorised form, while for the remaining families considered it consists of sums of factorised terms. Their zeros have a remarkable structure as the modulus of their product always equals unity.