4 citations · 8 across the 12 of their papers we have counts for
14 papers
Super-Arrhenius relaxation of the triangular plaquette model in any dimension
Laurent Bartholdi, Ivailo Hartarsky, Ivan Mitrofanov
Consider the following plaquette model from statistical physics: a lamp lies at every vertex of the triangular lattice and a switch lies at every even vertex of the (bipartite) dua…
Triangle covering problems and the Viterbo inequality in the plane
Alexey Balitskiy, Ivan Mitrofanov, Alexander Polyanskii
We review a certain problem on covering triangles in the plane. Equivalently, it can be viewed as a family of 'isobilliard' inequalities in convex shapes, and as a special case of…
Finite dimensional amenable groups
Anna Erschler, Ivan Mitrofanov
We show that an amenable group of finite Assouad-Nagata dimension satisfies the property of Shalom. Such infinite groups are known to admit a virtual homomorphism onto $\m…
Factor Complexity of the Most Significant Digits of~
Mehdi Golafshan, Ivan Mitrofanov
We investigate unipotent dynamics on a torus and apply these techniques to the following problem. Let \(d\) be a positive integer, and let \(a > 0\) be a real number. For an intege…
Total orders on compact metric spaces and covering dimension
Ivan Mitrofanov
We prove that for a compact metric space the property of having finite covering dimension is equivalent to the existence of a total order with finite snake number.
Assouad-Nagata dimension and gap for ordered metric spaces
Anna Erschler, Ivan Mitrofanov
We prove that all spaces of finite Assouad-Nagata dimension admit a good order for Travelling Salesman Problem, and provide sufficient conditions under which the converse is true.…
Spaces that can be ordered effectively: virtually free groups and hyperbolicity
Anna Erschler, Ivan Mitrofanov
We study asymptotic invariants of metric spaces, defined in terms of the travelling salesman problem, and our goal is to classify groups and spaces depending on how well they can b…
On cogrowth function of algebras and its logarithmical gap
A. J. Kanel-Belov, I. A. Melnikov, I. V. Mitrofanov
Let be an associative algebra. A finite word over alphabet is {\it-reducible} if its image in is a -linear combination of length-lexi…
On cogrowth function of uniformly recurrent sequences
Igor Melnikov, Ivan Mitrofanov
For a sequence we count the number of minimal forbidden words no longer then and prove that
On the existence of free subsemigroups in reversible automata semigroups
Dominik Francoeur, Ivan Mitrofanov
We prove that the semigroup generated by a reversible Mealy automaton contains a free subsemigroup of rank two if and only if it contains an element of infinite order.
The word and order problems for self-similar and automata groups
Laurent Bartholdi, Ivan Mitrofanov
We prove that the word problem is undecidable in functionally recursive groups, and that the order problem is undecidable in automata groups, even under the assumption that they ar…
Periodicity of Rauzy Scheme for substitution words
Alexei Kanel-Belov, Ivan Mitrofanov
From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arches. This notion is a tool to describe Rauzy graph behavior. F…
Periodicity of Rauzy scheme and substitutional systems
Alexei Kanel-Belov, Ivan Mitrofanov
In the paper the notion of {\em Rauzy scheme} is introduced. From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arch…
Inverse problems of symbolic dynamics
A. Ya. Belov, G. V. Kondakov, I. Mitrofanov
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for inves…