Recent Submissions

  • On the diameter of random planar graphs 

    Chapuy, G.; Fusy, Éric; Giménez Llach, Omer; Noy Serrano, Marcos (2015)
    Article
    Open Access
    We show that the diameter diam(Gn) of a random labelled connected planar graph with n vertices is equal to n1/4+o(1) , in probability. More precisely, there exists a constant c > 0 such that {equation presented} for ˜ small ...
  • Group-theoretic orbit decidability 

    Ventura Capell, Enric (De Gruytr, 2014-12-01)
    Article
    Restricted access - publisher's policy
    A recent collection of papers in the last years have given a renovated interest to the notion of orbit decidability. This is a new quite general algorithmic notion, connecting with several classical results, and closely ...
  • An involution on bicubic maps and beta(0,1)-trees 

    Claesson, Anders; Kitaev, Sergey; Mier Vinué, Anna de (2015)
    Article
    Open Access
    Bicubic maps are in bijection with (0 ; 1)-trees. We introduce two new ways of decomposing (0 ; 1)-trees. Using this we de ne an endofunc- tion on (0 ; 1)-trees, and thus also on bicubic maps. We show that ...
  • Fixed subgroups in free groups: a survey 

    Ventura Capell, Enric (2002-03)
    Article
    Open Access
    This note is a survey of the main results known about fixed subgroups of endomorphisms of finitely generated free groups. A historic point of view is taken, emphasizing the evolution of this line of research, from ...
  • On automorphism-fixed subgroups of a free group 

    Martino, Armando; Ventura Capell, Enric (2000-08)
    Article
    Open Access
    Let F be a flnitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphism-flxed, or auto-flxed for short, if there exists a set S of automorphisms of F such that H is precisely the ...
  • Twisted conjugacy in braid groups 

    Gonzalez Meneses, Juan; Ventura Capell, Enric (2014-01-01)
    Article
    Open Access
    In this note we solve the twisted conjugacy problem for braid groups, i.e., we propose an algorithm which, given two braids u,v is an element of B-n and an automorphism phi is an element of Aut(B-n), decides whether v = ...
  • A description of auto-fixed subgroups in a free group 

    Martino, Armando; Ventura Capell, Enric (2004-06)
    Article
    Open Access
    Let F be a finitely generated free group. By using Bestvina-Handel theory, as well as some further improvements, the eigengroups of a given automorphism of F (and its fixed subgroup among them) are globally analyzed and ...
  • Statistical properties of subgroups of free groups 

    Bassino, Frederique; Martino, Armando; Nicaud, Cyril; Ventura Capell, Enric; Weil, Pascal (2013-02-04)
    Article
    Open Access
    The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated ...
  • A Whitehad algorithm for toral relatively hyperbolic groups 

    Kharlampovich, Olga; Ventura Capell, Enric (2012-12-04)
    Article
    Open Access
    The Whitehead problem is solved in the class of toral relatively hyperbolic groups G (i.e. torsion-free relatively hyperbolic groups with abelian parabolic subgroups): there is an algorithm which, given two nite ...
  • The conjugacy problem in automaton groups is not solvable 

    Šunic, Z.; Ventura Capell, Enric (2012-08-15)
    Article
    Open Access
    (Free abelian)-by-free, self-similar groups generated by finite self-similar sets of tree automorphisms and having unsolvable conjugacy problem are constructed. Along the way, finitely generated, orbit undecidable, free ...

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