Increasing Diamonds

  • Olivier Bodini
  • Matthieu Dien
  • Xavier Fontaine
  • Antoine Genitrini
  • Hsien-Kuei Hwang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)


A class of diamond-shaped combinatorial structures is studied whose enumerating generating functions satisfy differential equations of the form \(f'' = G(f)\), for some function G. In addition to their own interests and being natural extensions of increasing trees, the study of such DAG-structures was motivated by modelling executions of series-parallel concurrent processes; they may also be used in other digraph contexts having simultaneously a source and a sink, and are closely connected to a few other known combinatorial structures such as trees, cacti and permutations. We explore in this extended abstract the analytic-combinatorial aspect of these structures, as well as the algorithmic issues for efficiently generating random instances.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Olivier Bodini
    • 1
  • Matthieu Dien
    • 2
  • Xavier Fontaine
    • 1
  • Antoine Genitrini
    • 2
  • Hsien-Kuei Hwang
    • 3
  1. 1.Laboratoire d’Informatique de Paris-NordCNRS UMR 7030 - Institut Galilée - Université Paris-NordVilletaneuseFrance
  2. 2.Sorbonne Universités, UPMC Univ Paris 06, CNRS, LIP6 UMR 7606ParisFrance
  3. 3.Institute of Statistical ScienceAcademia SinicaTaipeiTaiwan

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