101 citations · 968 across the 80 of their papers we have counts for
5 papers · 1 filter
Gröbner bases for operads
Vladimir Dotsenko, Anton Khoroshkin
We define a new monoidal category on collections (shuffle composition). Monoids in this category (shuffle operads) turn out to bring a new insight in the theory of symmetric operad…
On Superspace Actions for Multiple M2-Branes, Metric 3-Algebras and their Classification
Sergey A. Cherkis, Vladimir Dotsenko, Christian Saemann
We classify canonical metric 3-algebra structures on matrix algebras and find novel three-dimensional conformally invariant actions in N=4 projective superspace based on them. Thes…
Parking functions and vertex operators
Vladimir Dotsenko
We introduce several associative algebras and series of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for t…
A remark on Frobenius characters for set representations of symmetric groups
Vladimir Dotsenko
For any set representation (permutation representation) of the symmetric group , we give combinatorial interpretation for coefficients of its Frobenius character expanded in t…
An analogue of the Magnus problem for associative algebras
V. Dotsenko, N. Iyudu, D. Korytin
We prove an analogue of the Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by n+k generators and k relations and has an…