Related papers: Permutation monoids and MB-homogeneity for graphs …
We study permutations on n elements preserving orientation (parity) of every subset of size k. We describe all groups of these permutations. Unexpectedly, these groups (except for some special cases) are either trivial, cyclic or dihedral.…
We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.
We show that any graph product of residually finite monoids is residually finite. As a special case we obtain that any free product of residually finite monoids is residually finite. The corresponding results for graph products of…
We construct via Fra\"iss\'e amalgamation an $\omega$-categorical structure whose automorphism group is an infinite oligomorphic Jordan primitive permutation group preserving a `limit of $D$-relations'. The construction is based on a…
We study algebraic structure of the $\lambda$-polycyclic monoid $P_{\lambda}$ and its topologizations. We show that the $\lambda$-polycyclic monoid for an infinite cardinal $\lambda\geqslant 2$ has similar algebraic properties so has the…
A homogeneous family of subsets over a given set is one with a very ``rich'' automorphism group. We prove the existence of a bi-universal element in the class of homogeneous families over a given infinite set and give an explicit…
The group of automorphisms of the Brandt $\lambda^0$-extension $B^0_\lambda(S)$ of an arbitrary monoid $S$ with zero is described. In particular we show that the group of automorphisms $\mathbf{Aut}(B_{\lambda}^0(S))$ of $B_{\lambda}^0(S)$…
We investigate the dynamics of forward or backward self-similar systems (iterated function systems) and the topological structure of their invariant sets. We define a new cohomology theory (interaction cohomology) for forward or backward…
A finite graph $\Gamma$ is called $G$-symmetric if $G$ is a group of automorphisms of $\Gamma$ which is transitive on the set of ordered pairs of adjacent vertices of $\Gamma$. We study a family of symmetric graphs, called the unitary…
Given a finite alphabet X and an ordering on the letters, the map \sigma sends each monomial on X to the word that is the ordered product of the letter powers in the monomial. Motivated by a question on Groebner bases, we characterize…
We consider the general question of how the homological finiteness property left-FPn holding in a monoid influences, and conversely depends on, the property holding in the substructures of that monoid. In particular we show that left-FPn is…
We present an example of two countable $\omega$-categorical structures, one of which has a finite relational language, whose endomorphism monoids are isomorphic as abstract monoids, but not as topological monoids -- in other words, no…
A fully invarient congruence relations on the free algebra on a given type induces a variety of the given type. In contrast, a congruence relation of the free algebra provides algebra of that type. This algebra is given by a so-called…
The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A finite semigroup embeds in a real hyperplane face monoid if…
We describe the spreading property for finite transitive permutation groups in terms of properties of their associated coherent configurations, in much the same way that separating and synchronising groups can be described via properties of…
We introduce `braidability' as a new symmetry for (infinite) sequences of noncommutative random variables related to representations of the braid group $B_\infty$. It provides an extension of exchangeability which is tied to the symmetric…
In this article, we investigate the topological structure of large scale interacting systems on infinite graphs, by constructing a suitable cohomology which we call the uniform cohomology. The central idea for the construction is the…
The random permutation is the Fra\"iss\'e limit of the class of finite structures with two linear orders. Answering a problem stated by Peter Cameron in 2002, we use a recent Ramsey-theoretic technique to show that there exist precisely 39…
Let $T$ be a first-order theory. A correspondence is established between internal covers of models of $T$ and definable groupoids within $T$. We also consider amalgamations of independent diagrams of algebraically closed substructures, and…
The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the Benjamini-Schramm convergence for sparse structures. It is known that every first order convergent…