An Analogue of Distributivity for Ungraded Lattices

Thomas, Hugh (2006). « An Analogue of Distributivity for Ungraded Lattices ». Order, 23(2-3), pp. 249-269.

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Résumé

In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive. Trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Other than distributive lattices, the main examples of trim lattices are the Tamari lattices and various generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim, and we conjecture that all Cambrian lattices are trim.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	Left modular lattice, extremal lattice, supersolvable lattice, Tamari lattice, Cambrian lattice
Unité d'appartenance:	Faculté des sciences > Département de mathématiques
Déposé par:	Hugh R. Thomas
Date de dépôt:	24 mai 2016 15:11
Dernière modification:	30 mai 2016 20:23
Adresse URL :	http://archipel.uqam.ca/id/eprint/8506

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