A. Klyachko

activity

20242026

collaborators

6 papers

math.CO2026

Invariant covers of multipartite hypergraphs

Anton A. Klyachko, Mikhail S. Terekhov

We prove the following ``symmetric analogue'' of LovÃ¡sz's estimate (1975): if an $r$ -partite hypergraph of rank $r ⩾ 2$ has a cover of cardinality $n < \infty$ , then it admits…

math.CO2026

Invariant systems of weighted representatives

Anton A. Klyachko, Mikhail S. Terekhov

It is known that, if removing some $n$ edges from a graph $I^$ destroys all subgraphs isomorphic to a given finite graph $K$ , then all subgraphs isomorphic to $K$ can be destroyed…

math.GT2025

Tiny non-Leighton complexes

Natalia S. Dergacheva, Anton A. Klyachko

How complex must two finite 2-complexes be to admit a common, but not finite common, covering? We obtain an almost answer: the minimum possible number of triangles in a pseudo-simp…

math.GR2025

Equationally separable classes of groups

Alexander Buturlakin, Anton Klyachko, Denis Osin

Over each nontrivial finite group $G$ , there exists a finite system of equations having no solutions in larger finite groups but having a solution in a periodic group containing $G…

math.GT2024

Forester's lattices and small non-Leighton complexes

Natalia S. Dergacheva, Anton A. Klyachko

We construct two CW-complexes $K$ and $L$ admitting a common, but not finite common, covering, where $K$ is homeomorphic to a complex with a single 2-cell.

math.GR2024

Finite symmetric groups are strongly verbally closed

Olga K. Karimova, Anton A. Klyachko

Answering a question of A. V. Vasil'ev, we show that each finite symmetric (or alternating) group $H$ is a retract of any group containing $H$ as a verbally closed subgroup.