Speaker:  William Dugan, U Mass Amherst

Title:        Faces of generalized Pitman-Stanley polytopes

Abstract:

The Pitman-Stanley polytope is a polytope whose integer

lattice points biject onto the set of plane partitions of a certain

shape with entries in {0 ,1}. In their original paper, Pitman and

Stanley further suggest a generalization of their construction depending

on $m \in {\mathbb N}$ whose integer lattice points biject onto the set

of plane partitions of the same shape having entries in  $\{ 0 , 1, ...

, m \}$. In this talk, we give further details of this

generalized Pitman-Stanley polytope, $PS_n^m(\vec{a})$,

demonstrating that it can be realized as the flow polytope of a certain

graph. We then use the theory of flow polytopes to describe the faces of

these polytopes and produce a recurrence for their f-vectors.

William Dugan is a student of Alejandro Morales who is funding this visit.