4 citations · 4 across the 5 of their papers we have counts for
10 papers
Garside Theory: a Composition--Diamond Lemma Point of View
Viktor Lopatkin
This paper shows how to obtain the key concepts and notations of Garside theory by using the Composition--Diamond lemma. We also show in some cases the greedy normal form is exactl…
Circle graphs (chord interlacement graphs) of Gauss diagrams: Descriptions of realizable Gauss diagrams, algorithms, enumeration
Abdullah Khan, Alexei Lisitsa, Viktor Lopatkin +1
Chord diagrams, under the name of Gauss diagrams, are used in low-dimensional topology as an important tool for studying curves or knots. Those Gauss diagrams that correspond to cu…
-derivations of Lie algebras and transposed Poisson algebras
Bruno Leonardo Macedo Ferreira, Ivan Kaygorodov, Viktor Lopatkin
A relation between -derivations of Lie algebras and transposed Poisson algebras was established. Some non-trivial transposed Poisson algebras with a certain Lie algebr…
The variety of dual mock-Lie algebras
Luisa M. Camacho, Ivan Kaygorodov, Victor Lopatkin +1
We classify all complex - and -dimensional dual mock-Lie algebras by algebraic and geometric way. Also we find all non-trivial complex -dimensional dual mock-Lie algebras.
Commutative Lie algebras and commutative cohomology in characteristic
Viktor Lopatkin, Pasha Zusmanovich
We discuss a version of the Chevalley--Eilenberg cohomology in characteristic , where the alternating cochains are replaced by symmetric ones.
Bipartite Graphs as Polynomials, and Polynomials as Bipartite Graphs (with a view towards dividing in )
Andrey Grinblat, Viktor Lopatkin
The aim of this paper is to show that any finite undirected bipartite graph can be considered as a polynomial , and any directed finite bipartite graph can be…