An analogue of distributivity for ungraded lattices
| dc.creator | Thomas, Hugh | |
| dc.date | 2005-02-14 | |
| dc.date | 2005-09-12 | |
| dc.date.accessioned | 2026-07-07T05:16:58Z | |
| dc.date.available | 2026-07-07T05:16:58Z | |
| dc.description | In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive. Trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Other than distributive lattices, the main examples of trim lattices are the Tamari lattices and various generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim, and we conjecture that all Cambrian lattices are trim. | |
| dc.description | 19 pages, 4 figures. Version 2 includes small improvements to exposition, corrections of typos, and a new section showing that if a group G acts on a trim lattice by lattice automorphisms, then the sublattice of L consisting of elements fixed by G is trim | |
| dc.identifier | https://arxiv.org/abs/math/0502278 | |
| dc.identifier | http://arxiv.org/abs/math/0502278 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74184 | |
| dc.subject | Combinatorics | |
| dc.subject | 06A35, 05E15 | |
| dc.title | An analogue of distributivity for ungraded lattices | |
| dc.type | text |