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Nous présentons une extension de la théorie des implications entre attributs binaires aux implications partielles. A partir de données expérimentales on s'intéresse non seulement aux implications (globales), mais aussi aux «implications avec quelques contre exemples». Les implications partielles offrent une possibilité d'extraire des informations supplémentaires. Elles permettent de «modéliser» la fréquence relative d'une implication, non-valide pour toutes les données, et donnent par conséquent...
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.
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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