1 citations · 2 across the 24 of their papers we have counts for
27 papers
A non-plain virtually free group with a strictly 2-geodetic Cayley graph
André Carvalho
We construct an explicit infinite virtually free group with a finite inverse-closed generating set whose Cayley graph is -geodetic but not geodetic. More pr…
Green languages and growth of free inverse monoids
Corentin Bodart, André Carvalho, Ana-Catarina C. Monteiro +1
Motivated by recent work on conjugacy languages in groups, we introduce a general framework for studying \emph{languages of representatives} associated to equivalence relations on…
Conjugacy languages in free inverse monoids
André Carvalho, Ana-Catarina C. Monteiro
We initiate the study of conjugacy languages in free inverse monoids. Motivated by the notion of conjugacy languages in groups and the study of conjugacy in semigroups, we introduc…
The Post Correspondence Problem for free groups is undecidable
André Carvalho
We prove that the Post Correspondence Problem for finitely generated free groups is undecidable, even when one of the two homomorphisms is injective and has finite-index image. Thi…
Rational dynamics of a prime-representing map
André Carvalho
We study the rational dynamics of the map , which appears in the recursive construction of the prime-representing constant of Fridman, Gar…
On fixed points and equalizers of injective endomorphisms of the free group at infinity
André Carvalho, Pedro V. Silva
We study equalizers and fixed points of monomorphisms of free groups at infinity. We show that the action of the equalizer of two monomorphisms on the regular points of the equaliz…
A language-theoretic approach to study the density of subsets in free groups
André Carvalho
In this paper, we study the density of subsets of nonabelian free groups using relative densities of languages. We start by proving some basic properties about the density of a lan…
Conjugacy languages and conjugacy growth relative to subsets of groups
André Carvalho, Ana-Catarina C. Monteiro
In this paper, we explore conjugacy languages when the base problem is the generalized conjugacy problem (with constraints): given and , does have a conjug…
On linguistic subsets of groups and monoids
André Carvalho, Carl-Fredrik Nyberg-Brodda
We study subsets of groups and monoids defined by language-theoretic means, generalizing the classical approach to the word problem. We expand on results by Herbst from 1991 to a m…
On generalized (twisted) conjugacy separability of some extensions of groups
André Carvalho
We introduce separability properties corresponding to generalized versions of the conjugacy, twisted conjugacy, Brinkmann and Brinkmann's conjugacy problems and how they relate whe…
Geodesic languages for rational subsets and conjugates in virtually free groups
André Carvalho, Pedro V. Silva
We prove that a subset of a virtually free group is rational if and only if the language of geodesic words representing its elements (in any generating set) is rational and that th…
On supratopologies, normalized families and Frankl conjecture
André Carvalho, António Machiavelo
We introduce some generalized topological concepts to deal with union-closed families, and show that one can reduce the proof of Frankl's conjecture to some families of so-called s…
Free-abelian by free groups: homomorphisms and algorithmic explorations
André Carvalho, Jordi Delgado
We obtain an explicit description of the endomorphisms of free-abelian by free groups together with a characterization of when they are injective and surjective. As a consequence w…
Orbit problems for free-abelian times free groups and related families
André Carvalho, Jordi Delgado
We prove that the Brinkmann Problems (BrP & BrCP) and the twisted-conjugacy Problem (TCP) are decidable for any endomorphism of a free-abelian times free (FATF) group Fn x Z^m. Fur…
Subsets of groups in public-key cryptography
André Carvalho, António Malheiro
We suggest the usage of algebraic subsets instead of subgroups in public-key cryptography. In particular, we present the subset version of two protocols introduced by Shpilrain and…
Computing centralizers in [f.g. free]-by-cyclic groups
André Carvalho
We prove that centralizers of elements in [f.g. free]-by-cyclic groups are computable. As a corollary we get that, given two conjugate elements in a [f.g. free]-by-cyclic group, th…
Decidability of the Brinkmann Problems for endomorphisms of the free group
André Carvalho, Jordi Delgado
We show that both the Brinkmann Problem (BrP) and the Brinkmann Conjugacy Problem (BrCP) are decidable for endomorphisms of the free group Fn.
On the dynamics of endomorphisms of the direct product of two free groups
André Carvalho
We prove that Brinkmann's problems are decidable for endomorphisms of : given and , it is decidable wh…
Quantifying Brinkmann's problem: relative -order and -spectrum
André Carvalho
We prove that the stable image of an endomorphism of a virtually free group is computable. For an endomorphism , an element and a subset , we say that the…
On the intersection of fixed subgroups of
André Carvalho
We prove that, although it is undecidable if a subgroup fixed by an automorphism intersects nontrivially an arbitrary subgroup of , there is an algorithm that, takin…
On generalized conjugacy and some related problems
André Carvalho
We establish a connection between the generalized conjugacy problem for a -by- group, , and two algorithmic problems for : the generali…
Algebraic and context-free subsets of subgroups
André Carvalho
We study the relation between the structure of algebraic and context-free subsets of a group G and that of a finite index subgroup H. Using these results, we prove that a kind of F…
Eventually fixed points of endomorphisms of virtually free groups
André Carvalho
We consider the subgroup of points of finite orbit through the action of an endomorphism of a virtually free group, with particular emphasis on the subgroup of eventually fixed poi…
On endomorphisms of automatic groups
André Carvalho
We propose two geometric versions of the bounded reduction property and find conditions for them to coincide. In particular, for the natural automatic structure on a hyperbolic gro…