Mathematics Faculty Proceedings, Presentations, Speeches, Lectures

Title

The Extreme Points of the Convex Polytope of Doubly Substochastic Matrices with Fixed Row Sums and Column Sums

Event Name/Location

9th Shanghai Conference on Combinatorics, Shanghai, China, May 24-28, 2017

Document Type

Conference Proceeding

Publication Date

5-27-2017

Abstract

Let Ωn be the set all of n × n doubly stochastic matrices. It is well-known that Ωn is a polytope whose extreme points are the n × n permutation matrices. Let Ωsn, Ωhsn and Ωπn,denote the sets of symmetric doubly stochastic matrices, Hankel symmetric doubly stochastic matrices and centrosymmetric doubly stochastic matrices respectively. It is clear that Ωsn , Ωhsn and Ωπn are sub-polytopes of Ωn : The extreme points of Ωsn and Ωhsn were discovered, while the extreme points of Ωπn were not characterized completely. We determine all the extreme points and give characterizations of the permutation matrices which generated the extreme points.

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

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