Poset edge-labellings and left modularity

McNamara, Peter et Thomas, Hugh (2006). « Poset edge-labellings and left modularity ». European Journal of Combinatorics, 27(1), pp. 101-113.

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Résumé

It is known that a graded lattice of rank n is supersolvable if and only if it has an EL-labelling where the labels along any maximal chain are exactly the numbers 1,2,…,n without repetition. These labellings are called Sn EL-labellings, and having such a labelling is also equivalent to possessing a maximal chain of left modular elements. In the case of an ungraded lattice, there is a natural extension of Sn EL-labellings, called interpolating labellings. We show that admitting an interpolating labelling is again equivalent to possessing a maximal chain of left modular elements. Furthermore, we work in the setting of an arbitrary bounded poset as all the above results generalize to this case.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	Supersolvable lattice; EL-labelling; Left modularity
Unité d'appartenance:	Faculté des sciences > Département de mathématiques
Déposé par:	Hugh R. Thomas
Date de dépôt:	18 mai 2016 19:50
Dernière modification:	30 mai 2016 20:15
Adresse URL :	http://archipel.uqam.ca/id/eprint/8492

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