# Discrete CATS Seminar

Date:

12/03/2018 - 2:00pm

Location:

745 Patterson Office Tower

Speaker(s) / Presenter(s):

Matias von Bell, U of Kentucky

Speaker: Matias von Bell

Title: The ASMCRY(n) Polytope: An Interesting Face of the Alternating Sign Matrix Polytope.

Abstract: This talk showcases some of the work done by Karola Meszaros, Alejandro Morales, and Jessica Strikerin their 2015 paper titled ``On Flow Polytopes, Order Polytopes, and Certain Faces of the Alternating Sign Matrix Polytope". The alternating sign matrix polytope is the convex hull of alternating sign matrices. We will focus on one of its faces known as the Alternating Sign Matrix Chan-Robbins-Yuen polytope (ASMCRY(n)). It is part of a larger family: The ASM-CRY family of polytopes. After a discussion of flow- and order polytopes, we'll prove that the polytopes in the ASM-CRY family are both flow- and order polytopes. Then using Stanley's results for order polytopes, we show that ASMCRY(n) has Catalan many vertices, and its volume is the number of Standard Young Tableaux of staircase shape.This is Matias von Bell's Masters Exam.

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