Posets of width two and skew Young diagrams

Abstract

Let $P$ be a finite poset of width two, i.e., with no three-element antichain. We associate with $P$ a skew Young diagram $\Upsilon(P)$ and discuss some of the properties of the map $\Upsilon$. In particular, if we regard $\Upsilon(P)$ as a poset in a standard way, then the linear extensions of $P$ are in bijection with the order ideals of $\Upsilon(P)$.