Recent Submissions

  • Counting outerplanar maps 

    Geffner, I.; Noy Serrano, Marcos (2017-04-13)
    Article
    Open Access
    A map is outerplanar if all its vertices lie in the outer face. We enumerate various classes of rooted outerplanar maps with respect to the number of edges and vertices. The proofs involve several bijections with lattice ...
  • Subgraph statistics in subcritical graph classes 

    Drmota, Michael; Ramos Garrido, Lander; Rué Perna, Juan José (2017-04-01)
    Article
    Restricted access - publisher's policy
    Let H be a fixed graph and math formula a subcritical graph class. In this paper we show that the number of occurrences of H (as a subgraph) in a graph in math formula of order n, chosen uniformly at random, follows a ...
  • A lower bound for the size of a Minkowski sum of dilates 

    Hamidoune, Yayha Old; Rué Perna, Juan José (2011-03-01)
    Article
    Restricted access - publisher's policy
    Let A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of several dilates was obtained by Bukh. The unique known exact bound concerns the sum |A + k·A|, where k is a prime and |A| is ...
  • Asymptotic enumeration of non-crossing partitions on surfaces 

    Rué Perna, Juan José; Sau, Ignasi; Thilikos Touloupas, Dimitrios (2013-03-01)
    Article
    Restricted access - publisher's policy
    We generalize the notion of non-crossing partition on a disk to general surfaces with boundary. For this, we consider a surface S and introduce the number CS(n) of noncrossing partitions of a set of n points laying on the ...
  • Outerplanar obstructions for the vertex feedback set 

    Rué Perna, Juan José; Thilikos Touloupas, Dimitrios; Stavropoulos, Konstantinos (2012-07-02)
    Article
    Restricted access - publisher's policy
    For k = 1, let Fk be the class of graphs that contains k vertices meeting all its cycles. The minor-obstruction set for Fk is the set obs(Fk) containing all minor-minimal graphs that do not belong to Fk. We denote by Yk ...
  • On the number of nonzero digits of some integer sequences 

    Cilleruelo, Javier; Luca, Florián; Rué Perna, Juan José; Zumalacárregui, Ana (2012-06-05)
    Article
    Open Access
    Let b = 2 be a fixed positive integer. We show for a wide variety of sequences {an}8n=1 that for most n the sum of the digits of an in base b is at least cb log n, where cb is a constant depending on b and on the sequence
  • Asymptotic study of subcritical graph classes 

    Drmota, Michael; Fusy, Éric; Kang, Mihyun; Kraus, Veronika; Rué Perna, Juan José (2011-12-01)
    Article
    Open Access
    We present a unified general method for the asymptotic study of graphs from the so-called subcritical graph classes, which include the classes of cacti graphs, outerplanar graphs, and series-parallel graphs. This general ...
  • On the error term of the logarithm of the lcm of quadratic sequences 

    Rué Perna, Juan José; Sarka, Paulius; Zumalacárregui, Ana (2013-01-09)
    Article
    Open Access
    We study the logarithm of the least common multiple of the sequence of integers given by 12 + 1, 2 2 + 1, . . . , n2 + 1. Using a result of Homma [4] on the distribution of roots of quadratic polynomials modulo primes we ...
  • Random cubic planar graphs revisited 

    Noy Serrano, Marcos; Requile, Clement; Rué Perna, Juan José (2016-10-18)
    Article
    Restricted access - publisher's policy
    The goal of our work is to analyze random cubic planar graphs according to the uniform distribution. More precisely, let G be the class of labelled cubic planar graphs and let gn be the number of graphs with n vertices
  • On the fractional Parts of a^n/n 

    Cilleruelo, Javier; Luca, Florian; Kumchev, Angel; Rué Perna, Juan José; Shparlinski, Igor (2013-09-30)
    Article
    Open Access
    We give various results about the distribution of the sequence {a n/n}n=1 modulo 1, where a = 2 is a fixed integer. In particular, we find and infinite subsequence A such that {a n/n}n¿A is well distributed. Also we show ...

View more