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.