DISCRETE CATS SEMINAR

Discrete CATS Seminar

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.

Date:
Location:
745 POT
Event Series:

Discrete CATS Seminar

Masters Exam

Speaker:  Chloé Napier, University of Kentucky

Title:     New Interpretations of the Two Higher Stasheff-Tamari Orders

Abstract:

In 1996, Edelman and Reiner defined the two higher Stasheff-Tamari orders on triangulations of cyclic polytopes and conjectured that they are equal. In 2021, Nicholas Williams defined new combinatorial interpretations of these two orders to make the definitions more similar. He builds upon the work by Oppermann and Thomas in the even dimensional case of giving an algebraic analog to these orders using higher Auslander-Reiten Theory. He then gives a completely new result for the odd dimensional case. In this talk, we will discuss the combinatorial interpretations of the even dimensional case and motivate the odd dimensional case and algebraic analog by example. 

Date:
Location:
745 POT

Discrete CATS Seminar

Masters Exam

Speaker:  Chloé Napier, University of Kentucky

Title:     New Interpretations of the Two Higher Stasheff-Tamari Orders

Abstract:

In 1996, Edelman and Reiner defined the two higher Stasheff-Tamari orders on triangulations of cyclic polytopes and conjectured that they are equal. In 2021, Nicholas Williams defined new combinatorial interpretations of these two orders to make the definitions more similar. He builds upon the work by Oppermann and Thomas in the even dimensional case of giving an algebraic analog to these orders using higher Auslander-Reiten Theory. He then gives a completely new result for the odd dimensional case. In this talk, we will discuss the combinatorial interpretations of the even dimensional case and motivate the odd dimensional case and algebraic analog by example. 

Date:
Location:
745 POT