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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)

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 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)

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)

- Alice Jacquot
- 2014

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)

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)

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