If a knot is represented by an m‐strand braid, then HOMFLY polynomial in representation R
is a sum over characters in all representations Q∈ R⊗ m. Coefficients in this sum are traces …

A bstract With the help of the evolution method we calculate all HOMFLY polynomials in all
symmetric representations [r] for a huge family of (generalized) pretzel links, which are made …

By now it is well established that the quantum dimensions of descendants of the adjoint
representation can be described in a universal form, independent of a particular family of …

A bstract Many knots and links in S 3 can be drawn as gluing of three manifolds with one or
more four-punctured S 2 boundaries. We call these knot diagrams as double fat graphs …

We discuss a connection of HOMFLY polynomials with Hurwitz covers and represent a
generating function for the HOMFLY polynomial of a given knot in all representations as …

A very simple expression is conjectured for arbitrary colored Jones and HOMFLY
polynomials of a rich (g+ 1)-parametric family of pretzel knots and links. The answer for the …

A bstract We present a universal knot polynomials for 2-and 3-strand torus knots in adjoint
representation, by universalization of appropriate Rosso-Jones formula. According to …

Arborescent knots are those which can be represented in terms of double fat graphs or
equivalently as tree Feynman diagrams. This is the class of knots for which the present …

Colored knot polynomials have a special Z-expansion in certain combinations of
differentials, which depend on the representation. The expansion coefficients are functions …

We provide new evidence that the tangle calculus and “evolution” are applicable to the
Khovanov polynomials for families of long braids inside the knot diagram. We show that …