Poset Edge-Labellings and Left Modularity
| dc.creator | McNamara, Peter | |
| dc.creator | Thomas, Hugh | |
| dc.date | 2002-11-07 | |
| dc.date | 2004-07-12 | |
| dc.date.accessioned | 2026-07-07T06:21:56Z | |
| dc.date.available | 2026-07-07T06:21:56Z | |
| dc.description | 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 S_n 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 S_n 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. | |
| dc.description | 16 pages, 5 figures. Some minor expository changes. To appear in the European Journal of Combinatorics. A new bonus section not included in the published version introduces the non-straddling partitions of [n], a subset of the non-nesting partitions of [n]. We show that the non-straddling partitions of [n] form a lattice possessing a maximal chain of left modular elements | |
| dc.identifier | https://arxiv.org/abs/math/0211126 | |
| dc.identifier | http://arxiv.org/abs/math/0211126 | |
| dc.identifier | European Journal of Combinatorics 27 (1) (2006), 101-113 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95759 | |
| dc.subject | Combinatorics | |
| dc.subject | 06B99 (Primary) 06A11 (Secondary) | |
| dc.title | Poset Edge-Labellings and Left Modularity | |
| dc.type | text |