Crowns, Fences, and Dismantlable Lattices

Abstract

A finite lattice L of order n is dismantlable [6] if there is a chain L 1 ⊂ L 2 ⊂ . . . ⊂ L n = L of sublattices of L such that | L i | = i for every i = 1, 2, . . . , n . In [1] it was shown that every finite planar lattice is dismantlable. Furthermore, every lattice L with | L | ≦ 7 is dismantlable [6]; in fact, every large enough lattice contains a dismantlable sublattice with precisely n elements [4]. As well, such lattices are closed under the formation of sublattices and homomorphic images [6].