57 citations · 191 across the 13 of their papers we have counts for
13 papers
Khovanov complexes for bipartite links
A. Anokhina, E. Lanina, A. Morozov
Recently, for a limited class for bipartite links, the complicated Khovanov-Rozansky matrix factorization technique was reduced to an analogue of elementary Kauffman-Khovanov cycle…
Analogue of Goeritz matrices for computation of bipartite HOMFLY-PT polynomials
A. Anokhina, D. Korzun, E. Lanina +1
The Goeritz matrix is an alternative to the Kauffman bracket and, in addition, makes it possible to calculate the Jones polynomial faster with some minimal choice of a checkerboard…
Khovanov-Rozansky cycle calculus for bipartite links
A. Anokhina, E. Lanina, A. Morozov
Bipartite calculus is a direct generalization of Kauffman planar expansion from to arbitrary , applicable to the restricted class of knots which are entirely made of antip…
Bipartite expansion beyond biparticity
A. Anokhina, E. Lanina, A. Morozov
The recently suggested bipartite analysis extends the Kauffman planar decomposition to arbitrary , i.e. extends it from the Jones polynomial to the HOMFLY polynomial. This provi…
Planar decomposition of bipartite HOMFLY polynomials in symmetric representations
A. Anokhina, E. Lanina, A. Morozov
We generalize the recently discovered planar decomposition (Kauffman bracket) for the HOMFLY polynomials of bipartite knot/link diagrams to (anti)symmetrically colored HOMFLY polyn…
Planar decomposition of the HOMFLY polynomial for bipartite knots and links
A. Anokhina, E. Lanina, A. Morozov
The theory of the Kauffman bracket, which describes the Jones polynomial as a sum over closed circles formed by the planar resolution of vertices in a knot diagram, can be straight…
Towards tangle calculus for Khovanov polynomials
A. Anokhina, E. Lanina, A. Morozov
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 jumps…
Nimble evolution for pretzel Khovanov polynomials
Aleksandra Anokhina, Alexei Morozov, Aleksandr Popolitov
We conjecture explicit evolution formulas for Khovanov polynomials for pretzel knots in some regions in the windings space. Our description is exhaustive for genera 1 and 2. As pre…
Are Khovanov-Rozansky polynomials consistent with evolution in the space of knots?
A. Anokhina, A. Morozov
-coloured knot polynomials for -strand torus knots are described by the Rosso-Jones formula, which is an example of evolution in with Lyapunov exponents,…
Towards formalization of the soliton counting technique for the Khovanov-Rozansky invariants in the deformed -matrix approach
A. Anokhina
We consider recently developed Cohomological Field Theory soliton counting diagram technique for Khovanov and Khovanov-Rozansky invariants [1,2]. Although the expectation to obtain…
On R-matrix approaches to knot invariants
A. Anokhina
We present an elementary introduction to one of the most important today knot theory approaches, which gives rise to a representation for a class of knot polynomials in terms of qu…
Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary -deformation of HOMFLY
A. Anokhina, A. Morozov
We elaborate on the simple alternative from arXiv:1308.5759 to the matrix-factorization construction of Khovanov-Rozansky (KR) polynomials for arbitrary knots and links in the fund…
Racah coefficients and extended HOMFLY polynomials for all 5-, 6- and 7-strand braids
A. Anokhina, A. Mironov, A. Morozov +1
Basing on evaluation of the Racah coefficients for SU_q(3) (which supported the earlier conjecture of their universal form) we derive explicit formulas for all the 5-, 6- and 7-str…