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Eugenia Kochubinska

Publications and source records attributed to Eugenia Kochubinska.

5 recordsLinked to original sources
arXiv2020

On isomorphisms of $\mathcal{R}$- and $\mathcal{L}$-cross-sections of wreath products of finite inverse symmetric semigroups

We classify $\mathcal{R}$- and $\mathcal{L}$-cross-sections of wreath products of finite inverse symmetric semigroups $\mathcal{IS}_m \wr_p \mathcal{IS}_n$ up to isomorphism. We show that every isomorphism of $\mathcal{R}$ ($\mathcal{L}$-) cross-sections of $\mathcal{IS}_m \wr_p \mathcal{IS}_n$ is a conjugacy. As an auxiliary result, we get that every isomorphism of $\mathcal{R}$- ($\mathcal{L}$-) cross-sections of $\mathcal{IS}_n$ is also a conjugacy. We also compute the number of non-isomorphic $\mathcal{R}$- ($\mathcal{L}$-) cross-sections of $\mathcal{IS}_m \wr_p \mathcal{IS}_n$.

math.GR↗
arXiv2020

On cross-sections of partial wreath product of inverse semigroups

We classify $\mathcal{R}$- and $\mathcal{L}$-cross-sections of partial wreath product of inverse semigroups. As a corollary, we get the description of $\mathcal{R}$- and $\mathcal{L}$-cross-sections of the semigroupof partial automorphisms of finite regular rooted tree and compute also the number of different $\mathcal{R}$- ($\mathcal{L}$-) cross-sections in this semigroup.

math.GR↗
arXiv2020

Spectral properties of partial automorphisms of binary rooted tree

We study asymptotics of the spectral measure of a randomly chosen partial automorphism of a rooted tree. To every partial automorphism $x$ we assign its action matrix $A_x$. It is shown that the uniform distribution on eigenvalues of $A_x$ converges weakly in probability to $δ_0$ as $n \to \infty$, where $δ_0$ is the delta measure concentrated at $0$.

math.GR↗
arXiv2020

Spectrum of partial automorphisms of regular rooted tree

We study properties of eigenvalues of a matrix associated with a randomly chosen partial automorphism of a regular rooted tree. We show that asymptotically, as the numbers of levels goes to infinity, the fraction of non-zero eigenvalues converges to zero in probability.

math.GR↗