Partially ordered sets with nondistributive lattices of maximal antichains

Abstract

All partially ordered sets which are dealt with in the present paper are assumed to be finite.For a partially ordered set X we denote by MA(X) the system of all maximal antichains in X\ this system is considered to be partially ordered (cf.Section 1 below).Then MA(X) is a lattice (cf.[1]).A convex subset of X which is isomorphic to the partially ordered set on Fig. 1 or Fig. 2 will be called a serpentine set or a serpentine cycle in X, respectively.