2019/10/29 by Lei Cao, Cao, Lei, Darian McLaren +3
Chemistry · Computer Science · Mathematics · #05C35 #15B51 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Molecular spectroscopy and chirality #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1910.13490
openalex publication_date 2019/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider the convex set Γm,n of m× n stochastic matrices and the convex set Γm,nπ⊂ Γm,n of m× n centrosymmetric stochastic matrices (stochastic matrices that are symmetric under rotation by 180 degrees). For Γm,n, we demonstrate a Birkhoff theorem for its extreme points and create a basis from certain (0,1)-matrices. For Γm,nπ, we characterize its extreme points and create bases, whose construction depends on the parity of m, using our basis construction for stochastic matrices. For each of Γm,n and Γm,nπ, we further characterize their extreme points in terms of their associated bipartite graphs, we discuss a graph parameter called the fill and compute it for the various basis elements, and we examine the number of vertices of the faces of these sets. We provide examples illustrating the results throughout.