Leonid Bedratyuk

activity

20242026

collaborators

9 papers

math.RA2026

Projective Differential Moment Invariants from the Viewpoint of Classical Invariant Theory

Leonid Bedratyuk

Polynomial first-order projective differential moment invariants are investigated. The main result establishes an exact correspondence between such moment invariants and symmetric…

math.RA2026

Polynomial joint first-order differential projective invariants

Leonid Bedratyuk

We study polynomial absolute and relative joint first-order differential projective invariants for configurations of $n$ points in the plane. The main approach is based on passing…

math.CO2026

The Action of the Lie Algebra $sl_{n}$ on Colored Graphs and Multicolored Johnson Graphs

Leonid Bedratyuk

We consider the space of $(n - 1)$ -colored graphs on a fixed set of $N$ vertices. Each edge position of the complete graph $K_{N}$ has $n$ possible states: the absence of an edge and $…

math.CO2026

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…

math.CO2026

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…

math.RA2026

Relative Invariants from Moving Frames on an Extended Manifold

Leonid Bedratyuk

A constructive modification of the moving frame method is developed in this paper for the construction of relative invariants of regular Lie group actions. Let a relative invariant…

math.RA2025

Joint Projective Invariants on First Jet Spaces of Point Configurations via Moving Frames

Leonid Bedratyuk

We consider the action of the projective group $P G L (3, R)$ on the $n$ -fold first-order jet space of point configurations on the plane. Using the method of moving frames, we…

math.RA2025

First order joint differential projective invariants

Leonid Bedratyuk

We present a complete algebraic description of the field of first-order joint projective invariants for configurations of $ n $ points in the plane, under the natural diagonal ac…

math.CO2024

The $sl_{2}$ -actions on the symmetric polynomials and on Young diagrams

Leonid Bedratyuk

In the article, two implementations of the representation of the complex Lie algebra $sl_{2}$ on the algebra of symmetric polynomials $Λ_{n}$ by differential operators are p…

Projective Differential Moment Invariants from the Viewpoint of Classical Invariant Theory

Polynomial joint first-order differential projective invariants

The Action of the Lie Algebra sln​ on Colored Graphs and Multicolored Johnson Graphs

The Graph Algebra I: Representation-Theoretic Structure

Discrete Moving Frames, Semi-Algebraic Invariants and the Graph Canonization Problem

Relative Invariants from Moving Frames on an Extended Manifold

Joint Projective Invariants on First Jet Spaces of Point Configurations via Moving Frames

First order joint differential projective invariants

The sl2​-actions on the symmetric polynomials and on Young diagrams

The Action of the Lie Algebra $sl_{n}$ on Colored Graphs and Multicolored Johnson Graphs

The $sl_{2}$ -actions on the symmetric polynomials and on Young diagrams