In memoriam: Philippe Flajolet, the father of analytic combinatorics
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In memoriam: Philippe Flajolet, the father of analytic combinatorics
Bruno Salvy, Robert Sedgewick, Michèle Soria, Wojciech Szpankowski, Brigitte Vallée (2012)
RAIRO - Theoretical Informatics and Applications
Influence of modeling structure in probabilistic sequential decision problems
Florent Teichteil-Königsbuch, Patrick Fabiani (2006)
RAIRO - Operations Research
Markov Decision Processes (MDPs) are a classical framework for stochastic sequential decision problems, based on an enumerated state space representation. More compact and structured representations have been proposed: factorization techniques use state variables representations, while decomposition techniques are based on a partition of the state space into sub-regions and take advantage of the resulting structure of the state transition graph. We use a family of probabilistic exploration-like...
Integer partitions, tilings of -gons and lattices
Matthieu Latapy (2002)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of -gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a -gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
Integer Partitions, Tilings of 2D-gons and Lattices
Matthieu Latapy (2010)
RAIRO - Theoretical Informatics and Applications
In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2D-gons (hexagons, octagons, decagons, etc.). We show that the sets of partitions, ordered with a simple dynamics, have the distributive lattice structure. Likewise, we show that the set of tilings of a 2D-gon is the disjoint union of distributive lattices which we describe. We also discuss the special case of linear integer partitions, for which other dynamical models exist.
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