Maximal dimensional partially ordered sets II. characterization of 2n-element posets with dimension n

AbstractIn this paper, we show that if a partially ordered set has 2n elements and has dimension n, then it is isomorphic to the set of n−1 element subsets and 1element subsets of a set, ordered by inclusion, or else it has six elements and is isomorphic to a partially ordered set we call the chevron or to its dual