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We prove that outer commutator words are uniformly concise, i.e. if an outer commutator word w takes m different values in a group G, then the order of the verbal subgroup w(G) is bounded by a function depending only on m and not on w or G.…

In this article we give a sufficient and necessary condition to determine wether or not an element of the free group induces a non-trivial element of the free Burnside group of sufficiently large odd exponent. This criterion can be stated…

We introduce and study Polish topologies on various spaces of countable enumerated groups, where an enumerated group is simply a group whose underlying set is the set of natural numbers. Using elementary tools and well known examples from…

We investigate the orbits of automaton semigroups and groups to obtain algorithmic and structural results, both for general automata but also for some special subclasses. First, we show that a more general version of the finiteness problem…

We prove a general divisibility theorem that implies, e.g., that, in any group, the number of generating pairs (as well as triples, etc.) is a multiple of the order of the commutator subgroup. Another corollary says that, in any associative…

Relying on the techniques and ideas from our recent paper [13], we prove several anti-classification results for various rigidity conditions in countable abelian and nilpotent groups. We prove three main theorems: (1) the rigid abelian…

We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…

This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…

We study correlation estimates of automatic sequences (that is, sequences computable by finite automata) with polynomial phases. As a consequence, we provide a new class of good weights for classical and polynomial ergodic theorems, not…

We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The proof is based on reducing the problem to showing amenability…

We prove a non-generosity theorem for proper cosets in groups of finite Morley rank and elaborate on the theory of Weyl groups in this context.

The postulate of independence of cause and mechanism (ICM) has recently led to several new causal discovery algorithms. The interpretation of independence and the way it is utilized, however, varies across these methods. Our aim in this…

We design and test a cone finding algorithm to robustly address nonlinear system analysis through differential positivity. The approach provides a numerical tool to study multi-stable systems, beyond Lyapunov analysis. The theory is…

We prove a Universal Coefficient Theorem for objects in the bootstrap class in the equivariant Kasparov category for a finite cyclic group of square-free order.

We present a tool that automates termination proofs for recursive definitions by mining existing termination theorems.

Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…

This is a report on our long term project to find an algorithm to decide if a finitely presented group has a non-trivial action on a tree.

We prove two conjectures on the automorphism group of a one-dimensional formal group law defined over a field of positive characteristic. The first is that if a series commutes with a nontorsion automorphism of the formal group law, then…

This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…

Given a group $G$ with bounded torsion that acts properly on a systolic complex, we show that every solvable subgroup of $G$ is finitely generated and virtually abelian of rank at most $2$. In particular this gives a new proof of the above…