The extreme points of certain polytopes of doubly substochastic matrices

Abstract

Let (Formula presented.) and (Formula presented.) denote the convex polytope of (Formula presented.) centrosymmetric doubly substochastic matrices and the convex polytope of (Formula presented.) symmetric and Hankel-symmetric doubly substochastic matrices, respectively. In this paper, we investigate and fully characterize the extreme points of (Formula presented.) and (Formula presented.) which generalizes the results by Brualdi and Cao in [Brualdi RA, Cao L. Symmetric, Hankel-symmetric, and centrosymmetric doubly stochastic matrices. ActaMath Vietnam. 2018;43:675–700].