Poset edge-labellings and left modularity

Authors:
Peter McNamara;Hugh Thomas
Affiliations:
Laboratoire de Combinatoire et d'Informatique Mathématique, Université du Québec à Montreal, Montréal (Québec), Canada;Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, Canada and Fields Institute, Toronto, ON, Canada
Venue:
European Journal of Combinatorics
Year:
2006

Citing 3
Cited 1

Left-modular elements of lattices

Journal of Combinatorial Theory Series A
EL-labelings, supersolvability and 0-Hecke algebra actions on posets

Journal of Combinatorial Theory Series A
Enumerative Combinatorics: Volume 1

Enumerative Combinatorics: Volume 1

Chains of modular elements and shellability

Journal of Combinatorial Theory Series A

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Abstract

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.