Stack and Queue Layouts of Posets

The stacknumber (queuenumber) of a poset is defined as the stacknumber (queuenumber) of its Hasse diagram viewed as a directed acyclic graph. Upper bounds on the queuenumber of a poset are derived in terms of its jumpnumber, its length, its width, and the queuenumber of its covering graph. A lower bound of $\Omega(\sqrt n)$ is shown for the queuenumber of the class of n-element planar posets. The queuenumber of a planar poset is shown to be within a small constant factor of its width. The stacknumber of n-element posets with planar covering graphs is shown to be $\Theta(n)$. These results exhibit sharp differences between the stacknumber and queuenumber of posets as well as between the stacknumber (queuenumber) of a poset and the stacknumber (queuenumber) of its covering graph.