4 citations · 4 across the 1 of their papers we have counts for
7 papers
Generalized Equidistant Chebyshev Polynomials and Alexander Knot Invariants
A. M. Pavlyuk
We introduce the generalized equidistant Chebyshev polynomials T(k,h) of kind k of hyperkind h, where k,h are positive integers. They are obtained by a generalization of standard a…
Polynomial Invariants of Torus Knots and (p,q)-Calculus
Anatoliy M. Pavlyuk
We introduce the deformed fermionic numbers, corresponding to the skein relations, the main characteristics of knots and links. These fermionic numbers allow one to restore the ske…
HOMFLY Polynomial Invariants of Torus Knots and Bosonic (q,p)-Calculus
A. M. Pavlyuk
For the one-parameter Alexander (Jones) skein relation we introduce the Alexander (Jones) "bosonic" q-numbers, and for the two-parameter HOMFLY skein relation we propose the HOMFLY…
Generalization of Polynomial Invariants and Holographic Principle for Knots and Links
A. M. Pavlyuk
We formulate the holographic principle for knots and links. For the "space" of all knots and links, torus knots T(2m+1,2) and torus links L(2m,2) play the role of the "boundary" of…
Generalized Alexander Polynomial Invariants
Anatoliy M. Pavlyuk
We propose an algorithm which allows to derive the generalized Alexander polynomial invariants of knots and links with the help of the q,p-numbers, appearing in bosonic two-paramet…
On T(n,4) torus knots and Chebyshev polynomials
A. M. Pavlyuk
The Alexander polynomials Δ_{n,3}(t) and Δ_{n,4}(t) are presented as a sum of the Alexander polynomials Δ_{k,2}(t). These polynomials are also expressed in the form of a sum of Che…