arXiv Open Access 2025

Enumeration and constructions of vertices of the polytope of polystochastic matrices

Anna A. Taranenko
Lihat Sumber

Abstrak

A multidimensional nonnegative matrix is called polystochastic if the sum of entries in each of its lines equals $1$. The set of all polystochastic matrices of order $n$ and dimension $d$ is a convex polytope $Ω_n^d$ known as the Birkhoff polytope. In this paper, we identify all vertices of the polytopes $Ω_4^3$ and $Ω_3^4$ correcting the results of Ke, Li, and Xiao (2016). Additionally, we describe constructions vertices of $Ω_n^d$ using multidimensional matrix products and find symmetric vertices of $Ω_3^d$ for all $d \geq 4$ with large support sizes.

Topik & Kata Kunci

Penulis (1)

A

Anna A. Taranenko

Format Sitasi

Taranenko, A.A. (2025). Enumeration and constructions of vertices of the polytope of polystochastic matrices. https://arxiv.org/abs/2502.09149

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2025
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓