Related papers: On generic properties of finitely presented monoid…
In this paper emphasis is placed on how the behavior of the solutions of a PDE is affected by the geometry of the generalized $m$-quasi-Einstein manifold, and vice versa. Considering a $n$-dimensional generalized $m$-quasi-Einstein manifold…
Birget, Margolis, Meakin and Weil proved that a finitely generated subgroup $K$ of a free group is pure if and only if the transition monoid $M(K)$ of its Stallings automaton is aperiodic. In this paper, we establish further connections…
Based on the work done in \cite{BV-Tind,DMS} in the o-minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking-independent elements that is dense inside a…
For a countable group $G$ we construct a small, idempotent complete, symmetric monoidal, stable $\infty$-category $\mathrm{KK}^{G}_{\mathrm{sep}}$ whose homotopy category recovers the triangulated equivariant Kasparov category of separable…
We study rewriting properties of the column presentation of plactic monoid for any semisimple Lie algebra such as termination and confluence. Littelmann described this presentation using L-S paths generators. Thanks to the shapes of…
Generalization problems in languages with binders involve computing the most common structure between expressions while respecting bound variable renaming and freshness constraints. These problems often lack a least general solution.…
We prove a quantitative refinement of the statement that groups of polynomial growth are finitely presented. Let $G$ be a group with finite generating set $S$ and let $\operatorname{Gr}(r)$ be the volume of the ball of radius $r$ in the…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coincides with the positive theory of a non-abelian free group.…
We initiate the study of expansions of monoids in the class of two-sided restriction monoids and show that generalizations of the Birget-Rhodes prefix group expansion, despite the absence of involution, have rich structure close to that of…
Around 1980 commutator theory was generalized from groups to arbitrary algebras using the socalled term condition commutator. The semigroups that are abelian with respect to this commutator were classified by Warne (1994). We study what…
We provide a geometric model for the free $X$-generated $F$-restriction semigroup in the extended signature $(\cdot\,, ^+, ^m,\lambda)$, where the unary operation $^m$ maps an element $a$ to the maximum element $a^m$ of its $\sigma$-class,…
We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of…
The standard $(n, k, d)$ model of random groups is a model where the relators are chosen randomly from the set of cyclically reduced words of length $k$ on an $n$-element generating set. Gromov's density model of random groups considers the…
We show that every finitely generated conical refinement monoid can be represented as the monoid $\mathcal V(R)$ of isomorphism classes of finitely generated projective modules over a von Neumann regular ring $R$. To this end, we use the…
We generalise a key result of one-relator group theory, namely Magnus's Freiheitssatz, to partially commutative groups, under sufficiently strong conditions on the relator. The main theorem shows that under our conditions, on an element $r$…
Let $H$ be a closed normal subgroup of a compact Lie group $G$ such that $G/H$ is connected. This paper provides a necessary and sufficient condition for every complex representation of $H$ to be extendible to $G$, and also for every…
Monoids generated by elements of order two appear in numerous places in the literature. For example, Coxeter reflection groups in geometry, Kuratowski monoids in topology, various monoids generated by regular operations in language theory…
Recent research of the author has given an explicit geometric description of free (two-sided) adequate semigroups and monoids, as sets of labelled directed trees under a natural combinatorial multiplication. In this paper we show that there…
We show that the Julia set of a non-elementary rational semigroup G is uniformly perfect when there is a uniform bound on the Lipschitz constants of the generators of G. This also proves that the limit set of a non-elementary Moebius group…