The Gluing Number of Ordered Sets

Abstract

For an ordered set \(A\) and \(B\) whose orders agree on its intersection, the gluing of \(A\) and \(B\) is defined to be the ordered set on the union of its underlying sets whose order is the transitive closure of the union of the orders of \(A\) and \(B\). The gluing number of an ordered set \(P\) is the minimum number of induced semichains (suborders of dimension at most two) of \(P\) whose consecutive gluing is \(P\). In this paper we investigate this parameter on some special ordered sets.