A combinatorial theory of Grünbaum's new regular polyhedra, Part I: Grünbaum's new regular polyhedra and their automorphism group.
A flat manifold with no symmetries.
A remark on the irreducible characters and fake degrees of finite real reflection groups.
Algebra of antisymmetric characteristics.
Almost-Bieberbach groups with prime order holonomy
The main issue of this paper is an attempt to find a decomposition theorem for infra-nilmanifolds in the same spirit as a result of A. Vasquez for flat Riemannian manifolds. That is: we look for infra-nilmanifolds with prime order holonomy which can be obtained as a fiber space with a non-trivial nilmanifold as fiber and an infra-nilmanifold as its base. In this perspective, we prove the following algebraic result: if E is an almost-Bieberbach group with prime order holonomy,...
An approach to zeta-function of finite factorgraph via the Markov topological chains
Arrangements Defined by Unitary Reflection Groups.
Artin-Gruppen und Coxeter-Gruppen.
Automatic stochastic control of impulses on a three-dimensional crystallographic lattice
Automorphism groups of compact Klein surfaces with one boundary component.
Automorphism Groups of Compact Planar Klein Surfaces.
Bounds for quaternionic line systems and reflection groups.
Calculating canonical distinguished involutions in the affine Weyl groups.
Chromatic Plane Compositions
Coarse structures and group actions
The main results of the paper are: Proposition 0.1. A group G acting coarsely on a coarse space (X,𝓒) induces a coarse equivalence g ↦ g·x₀ from G to X for any x₀ ∈ X. Theorem 0.2. Two coarse structures 𝓒₁ and 𝓒₂ on the same set X are equivalent if the following conditions are satisfied: (1) Bounded sets in 𝓒₁ are identical with bounded sets in 𝓒₂. (2) There is a coarse action ϕ₁ of a group G₁ on (X,𝓒₁) and a coarse action ϕ₂ of a...
Computation of five- and six-dimensional Bieberbach groups.
Computational aspects of group extensions and their applications in topology.
Congruence, Similarity, and Symmetries of Geometric Objects.
Constructing irreducible representations of Weyl groups.
Counting crystallographic groups in low dimensions.