49 citations · 56 across the 13 of their papers we have counts for
15 papers
On the generating function and growth of the positive singular braid monoid
A. L. Anisimov, G. A. Kameneva, V. V. Vershinin
We prove that the generating function of the positive singular braid monoid is rational and we give the exact formula for such monoid on three strands.
Path homology of directed hypergraphs
Yuri Muranov, Anna Szczepkowska, Vladimir Vershinin
We describe various path homology theories constructed for a directed hypergraph. We introduce the category of directed hypergraphs and the notion of a homotopy in this category. A…
On homotopy braids
V. G. Bardakov, V. V. Vershinin, Jie Wu
Homotopy braid group is the subject of the paper. First, linearity of homotopy braid group over the integers is proved. Then we prove that the group homotopy braid group on three s…
On addition theorems related to elliptic integrals
Malkhaz Bakuradze, Vladimir Vershinin
This paper provides some explicit formulas related to addition theorems for elliptic integrals , where is the square root from a polynomial of degree 4. Th…
On Cohen braids
Valery Bardakov, Vladimir Vershinin, Jie Wu
For a general surface and an arbitrary braid from the surface braid group we study the system of equations where operation is de…
About presentations of braid groups and their generalizations
Vladimir V. Vershinin
In the paper we give a survey of rather new notions and results which generalize classical ones in the theory of braids. Among such notions are various inverse monoids of partial b…