Related papers: Etude des morphismes pr{\'e}servant les mots primi…

The classical homomorphism preservation theorem, due to {\L}o\'s, Lyndon and Tarski, states that a first-order sentence $\phi$ is preserved under homomorphisms between structures if, and only if, it is equivalent to an existential positive…

It it shown that geometric morphisms between elementary toposes can be represented as adjunctions between the corresponding categories of locales. These adjunctions are characterised as those that preserve the order enrichment, commute with…

Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of omega-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is…

A permutation of n letters is k-prolific if each (n-k)-subset of the letters in its one-line notation forms a unique pattern. We present a complete characterization of k-prolific permutations for each k, proving that k-prolific permutations…

A factorization of a permutation into transpositions is called "primitive" if its factors are weakly ordered. We discuss the problem of enumerating primitive factorizations of permutations, and its place in the hierarchy of previously…

We say that two finite words $u$ and $v$ are abelian equivalent if and only if they have the same number of occurrences of each letter, or equivalently if they define the same Parikh vector. In this paper we investigate various abelian…

Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…

We present the ideas behind an algorithm to compute normalizers of primitive groups with non-regular socle in polynomial time. We highlight a concept we developed called permutation morphisms and present timings for a partial implementation…

We study primitive stable representations of free groups into higher rank semisimple Lie groups and their properties. Let $\Sigma$ be a compact, connected, orientable surface (possibly with boundary) of negative Euler characteristic. We…

As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…

We prove that a sequence is primitive substitutive if and only if the set of its derived sequences is finite; we defined these sequences here.

In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of…

We investigate questions related to the presence of primitive words and Lyndon words in automatic and linearly recurrent sequences. We show that the Lyndon factorization of a k-automatic sequence is itself k-automatic. We also show that the…

Words can be represented by composing the representations of subword units such as word segments, characters, and/or character n-grams. While such representations are effective and may capture the morphological regularities of words, they…

Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…

We give several characterizations of Mersenne primes (Theorem 1.1) and of primes for which 2 is a primitive root (Theorem 1.2). These characterizations involve group algebras, circulant matrices, binomial coefficients, and bipartite graphs.

It is known that there are infinite words over finite alphabets with Abelian repetition threshold arbitrarily close to 1; however, the construction previously used involves huge alphabets. In this note we give a short cyclic morphism…

We show that for every $n \geq 1$ and over any finite alphabet, there is a word whose circular factors of length $n$ have a one-to-one correspondence with the set of primitive words. In particular, we prove that such a word can be obtained…

It is known that each word of length $n$ contains at most $n+1$ distinct palindromes. A finite rich word is a word with maximal number of palindromic factors. The definition of palindromic richness can be naturally extended to infinite…

Regular nested word languages (a.k.a. visibly pushdown languages) strictly extend regular word languages, while preserving their main closure and decidability properties. Previous works have shown that considering languages of 2-nested…