Symmetric, Hankel-symmetric, and Centrosymmetric Doubly Stochastic Matrices

TL;DR

This paper studies special classes of doubly stochastic matrices with symmetry properties, analyzing their geometric structure, extreme points, and basis of related permutation matrices.

Contribution

It characterizes the dimensions, extreme points, and bases of convex polytopes of symmetric, Hankel-symmetric, and centrosymmetric doubly stochastic matrices.

Findings

Dimensions of the polytopes are determined.

Extreme points are classified.

Bases of permutation matrices with these structures are identified.

Abstract

We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, Hankel symmetric, centrosymmetric, and both symmetric and Hankel symmetric. We determine dimensions of these polytopes and classify their extreme points. We also determine a basis of the real vector spaces generated by permutation matrices with these special structures.