49 citations · 56 across the 13 of their papers we have counts for
10 papers · 1 filter
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.
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…
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…
On Vassiliev invariants of braid groups of the sphere
N. Kaabi, V. V. Vershinin
We construct a universal Vassiliev invariant for braid groups of the sphere and the mapping class groups of the sphere with punctures. The case of a sphere is different from th…
Generating groups by conjugation-invariant sets
Valery Bardakov, Vladimir Tolstykh, Vladimir Vershinin
Let S be a generating set of a group G. We say that G has FINITE WIDTH relative to S if G=(S\cup S^{-1})^k for a suitable natural number k. We say that a group G is a group of FINI…
On the inverse braid and reflection monoids of type
V. V. Vershinin
There are well known relations between braid groups and symmetric groups, between Artin-Briskorn braid groups and Coxeter groups. Inverse braid monoid the same way is related to th…