51 citations · 254 across the 64 of their papers we have counts for
6 papers · 1 filter
General constructions of biquandles and their symmetries
Valeriy Bardakov, Timur Nasybullov, Mahender Singh
Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set-theor…
Multi-switches and representations of braid groups
Valeriy Bardakov, Timur Nasybullov
In the paper, we introduce the notion of a (virtual) multi-switch which generalizes the notion of a (virtual) switch. Using (virtual) multi-switches we introduce a general approach…
Computing skew left braces of small orders
Valeriy G. Bardakov, Mikhail V. Neshchadim, Manoj K. Yadav
We improve Algorithm 5.1 of [Math. Comp. {\bf 86} (2017), 2519-2534] for computing all non-isomorphic skew left braces, and enumerate left braces and skew left braces of orders up…
On virtual cabling and structure of 4-strand virtual pure braid group
Valeriy G. Bardakov, Jie Wu
This article is dedicate to cabling on virtual braids. This construction gives a new generating set for the virtual pure braid group . Consequently we describe as HNN-…
On embeddings of quandles into groups
Valeriy Bardakov, Timur Nasybullov
In the present paper, we introduce the new construction of quandles. For a group and its subset we construct a quandle which is called the -quandle and stud…
Link quandles are residually finite
Valeriy G. Bardakov, Mahender Singh, Manpreet Singh
Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work [2] residual finiteness of…