Boltzmann samplers are a kind of random samplers; in 2004, Duchon, Flajolet, Louchard and Schaeffer showed that given a combinatorial class and a combinatorial specification for that class, one can automatically build a Boltzmann sampler. In this paper, we introduce a Boltzmann sampler for Motzkin trees built from a holonomic specification, that is, a… (More)
We investigate the asymptotic number of elements of size n in a particular class of closed lambda-terms (so-called BCI(p)-terms) which are generalizations of lambda-terms related to axiom systems of combinatory logic. By deriving a differential equation for the generating function of the counting sequence we obtain a recurrence relation which can be solved… (More)
In this paper, we give a general framework for the Boltzmann generation of colored objects belonging to combinatorial constructible classes. We propose an intuitive notion called profiled objects which allows the sampling of size-colored objects (and also of k-colored objects) although the corresponding class cannot be described by an analytic ordinary… (More)
We present a new uniform random sampler for binary trees with n internal nodes consuming 2n + Θ(log(n) 2) random bits on average. This makes it quasi-optimal and out-performs the classical Remy algorithm. We also present a sampler for unary-binary trees with n nodes taking Θ(n) random bits on average. Both are the first linear-time algorithms to be optimal… (More)
Recent work of Brlek et al. gives a characterization of digitally convex polyominoes using combinatorics on words. From this work, we derive a combinatorial symbolic description of digitally convex polyominoes and use it to analyze their limit properties and build a uniform sampler. Experimentally , our sampler shows a limit shape for large digitally convex… (More)
j'oublie et plus généralement aux moisséens et tourangeaux, aux cirqueux et à tous les spammés de Jeux à Quincampoix, sans oublier toute ma grande famille. Et merci à Axel, puisque tu tiens à être mentionné, mais je crois que tu sais déjà tout le bien que je pense de toi et que je peux décemment écrire ici.
This paper is devoted to the random generation of particular colored necklaces for which the number of beads of a given color is constrained (these necklaces are called v-balanced). We propose an efficient sampler (its expected time complexity is linear) which satisfies the Boltzmann model principle introduced by Duchon, Flajolet, Louchard and Schaeffer… (More)