Random orders (Q1058533)

For fixed integers k and n and a set S of cardinality n let \(P_ k(n)\) be the partial order on S given by the intersection of k randomly and independently chosen linear orders on S. The author begins to study the basic parameters of \(P_ k(n)\) (as height, width, number of extremal elements) for fixed k and large n. His object is to illustrate some techniques for dealing with these random orders and to lay the groundwork for the future research, hoping that they will be found to have useful properties not obtainable by known constructions.