Large Minimal Realizers Of A Partial Order II
The rank (resp. dimension) of a poset P is the cardinality of a largest (resp. smallest) set of linear orders such that its intersection is P and no proper subset has intersection P. Dimension has been studied extensively. Rank was introduced recently by Maurer and Rabinovitch in , where the rank of antichains was determined. In this paper we develop a general theory of rank. The main result, loosely stated, is that to each poset P there corresponds a class of graphs with easily described properties, and that the rank of Pis the maximum number of edges in a graph in this class.
Stephen B. Maurer , '67; I. Rabinovitch; and W. T. Trotter Jr..
"Large Minimal Realizers Of A Partial Order II".