4 papers
A relation between the HOMFLY-PT and Kauffman polynomials via characters
Andreani Petrou, Shinobu Hikami
The HOMFLY-PT and Kauffman polynomials are related to each other for special classes of knots constructed by full twists and Jucys-Murphy twists. The conditions for this relation a…
Braid twists and HZ factorisation via character expansion
Andreani Petrou, Shinobu Hikami
The HOMFLY-PT polynomial of a closed braid admits a character expansion, expressed as a sum of SU(N) characters over Young diagrams. The Harer-Zagier (HZ) transform, which converts…
The HOMFLY-PT polynomial and HZ factorisation
Andreani Petrou, Shinobu Hikami
The Harer-Zagier (HZ) transform maps the HOMFLY-PT polynomial into a rational function. For some special knots and links, the latter admits a simple factorised form, which is refer…
Harer-Zagier formulas for families of twisted hyperbolic knots
Andreani Petrou, Shinobu Hikami
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 pol…