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 …

For a peculiar family of double braid knots there is a remarkable factorization formula for the
coefficients of the differential (cyclotomic) expansion (DE), which nowadays is widely used to …

We conjecture a closed-form expression of HOMFLY-PT invariants of double twist knots
colored by rectangular Young diagrams where the twist is encoded in interpolation …

Defect characterizes the depth of factorization of terms in differential (cyclotomic) expansions
of knot polynomials, ie of the non-perturbative Wilson averages in the Chern-Simons theory …

We outline the current status of the differential expansion (DE) of colored knot polynomials ie
of their Z–F decomposition into representation–and knot–dependent parts. Its existence is a …

We conjecture explicit evolution formulas for Khovanov polynomials, which for any particular
knot are Laurent polynomials of complex variables q and T, for pretzel knots of genus g in …

The differential expansion is one of the key structures reflecting group theory properties of
colored knot polynomials, which also becomes an important tool for evaluation of non-trivial …

Factorization of the differential expansion (DE) coefficients for colored HOMFLY-PT
polynomials of antiparallel double braids, originally discovered for rectangular …

The defect of differential (cyclotomic) expansion for colored HOMFLY-PT polynomials is
conjectured to be invariant under any antiparallel evolution and change linearly with the …

We claim that the recently discovered universal-matrix precursor for the F functions, which
define the differential expansion of colored polynomials for twist and double braid knots, can …