1 citations · 2 across the 24 of their papers we have counts for
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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…