4 papers · 1 filter
The Action of the Lie Algebra on Colored Graphs and Multicolored Johnson Graphs
Leonid Bedratyuk
We consider the space of -colored graphs on a fixed set of vertices. Each edge position of the complete graph has possible states: the absence of an edge and $…
The Graph Algebra I: Representation-Theoretic Structure
Leonid Bedratyuk
The paper studies the graph algebra whose monomial basis is naturally indexed by simple graphs on a fixed set of vertices. This algebra is at the same time the algebra of pseudo-Bo…
Discrete Moving Frames, Semi-Algebraic Invariants and the Graph Canonization Problem
Leonid Bedratyuk
This paper develops an invariant--geometric interpretation of the canonization problem for simple undirected weighted graphs based on the {discrete moving frame method} for finite…
The -actions on the symmetric polynomials and on Young diagrams
Leonid Bedratyuk
In the article, two implementations of the representation of the complex Lie algebra on the algebra of symmetric polynomials by differential operators are p…