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EJC
2006

Poset edge-labellings and left modularity

13 years 3 months ago
Poset edge-labellings and left modularity
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. 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. Version of 12 July 2004
Peter McNamara, Hugh Thomas
Added 12 Dec 2010
Updated 12 Dec 2010
Type Journal
Year 2006
Where EJC
Authors Peter McNamara, Hugh Thomas
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