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Displaying similar documents to “Enumeration of Lattice paths and generating functions for skew plane partitions.”

Classification systems and their lattice

Sándor Radeleczki (2002)

Discussiones Mathematicae - General Algebra and Applications

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We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent...

Integer partitions, tilings of 2 D -gons and lattices

Matthieu Latapy (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In this paper, we study two kinds of combinatorial objects, generalized integer partitions and tilings of 2 D -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 2 D -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. ...