Covering posets (Q1108294)

Let \((X,\leq)\) be an ordered set. A pair \((a,b)\) of elements of \(X\) is a covering pair if \(b\) covers \(a\). The set \(C(X)\) of all covering pairs of \(X\) can be naturally ordered by \((a,b)\leq (c,d)\) iff \((a,b)=(c,d)\) or \(b\leq c\). The poset \((C(X),\leq)\) is called the covering poset of \((X,\leq)\). The paper contains necessary and sufficient conditions for a finite poset to be a covering poset of a finite poset. The author also derives some relations between finite posets with isomorphic covering posets and some relations between dimensions of \((X,\leq)\) and \((C(X),\leq)\).