Eric Fusy

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  • J Erémie Bouttier, Eric Fusy, Emmanuel Guitter
  • 2014
We consider the problem of computing the distance-dependent two-point function of general planar maps and hypermaps, i.e. the problem of counting such maps with two marked points at a prescribed distance. The maps considered here may have faces of arbitrarily large degree, which requires new bijections to be tackled. We obtain exact expressions for the(More)
  • Philippe Flajolet, Eric Fusy, Carine Pivoteau
  • 2006
Boltzmann models from statistical physics combined with methods from analytic combinatorics give rise to efficient algorithms for the random generation of unlabelled objects. The resulting algorithms generate in an unbiased manner discrete configurations that may have nontrivial symmetries , and they do so by means of real-arithmetic computations. We(More)
It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is 1.104366∙n-3/2∙2.618034n. Motivated by the kinetics of RNA secondary structure formation, we are interested in determining the asymptotic number of secondary structures that are locally optimal, with respect to a particular energy model. In the Nussinov(More)
We determine the exact and asymptotic number of unlabeled outerplanar graphs. The exact number gn of unlabeled outerplanar graphs on n vertices can be computed in polynomial time, and gn is asymptotically g n −5/2 ρ −n , where g ≈ 0.00909941 and ρ −1 ≈ 7.50360 can be approximated. Using our enumerative results we investigate several statistical properties(More)
We present two quite different algorithms to compute the number of elements in the sphere of radius n of Thompson's group F with standard generating set. The first of these requires exponential time and polynomial space, but additionally computes the number of geodesics and is generalisable to many other groups. The second algorithm requires polynomial time(More)
In brief, this license authorizes each and everybody to share (to copy, distribute and transmit) the work under the following conditions, without impairing or restricting the authors' moral rights: Attribution: The work must be attributed to its authors. LIPIcs is a series of high-quality conference proceedings across all fields in informatics. LIPIcs(More)
Guided navigation [5] is fundamental for the Oracle Big Data Discovery product. Our customers need to know the most frequent elements in their datasets, and the number of elements of a particular kind. In Figure 1, for the winetype property, we use a query that returns the top 6 kinds of wines ('Red', a query that counts the number of distinct types of(More)
  • Eric Fusy, Ecole Polytechnique, Thibault Et, Maks J
  • 2015
Spécialité : Informatique soutenue et présentée publiquement le mardi 1 décembre 2015 par : Résumé. Nous présentons dans ce document un cadre bijectif pour les cartes planaires (graphes plongés sur la sphèrè a déformation continue près). Notre méthode repose sur une 'méta-bijection' entre certaines cartes (planaires) orientées et certaines structures(More)
Tutte has described in the book " Connectivity in graphs " a canonical decomposition of any graph into 3-connected components. In this article we translate (using the language of symbolic combinatorics) Tutte's decomposition into a general grammar expressing any family G of graphs (with some stability conditions) in terms of the subfamily G 3 of graphs in G(More)