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Article
Poset Edge-Labellings and Left Modularity
European Journal of Combinatorics
  • Peter R. W. McNamara, Bucknell University
  • Hugh Thomas
Publication Date
1-1-2006
Volume
27
Issue
1
Disciplines
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 a general bounded poset as all the above results generalize to this case. We conclude by applying our results to show that the lattice of non-straddling partitions, which is not graded in general, has a maximal chain of left modular elements.

Citation Information
Peter R. W. McNamara and Hugh Thomas. "Poset Edge-Labellings and Left Modularity" European Journal of Combinatorics (2006) p. 101 - 113
Available at: http://works.bepress.com/peter_mcnamara/15/