arXiv
Open Access
2025
Enumeration and constructions of vertices of the polytope of polystochastic matrices
Anna A. Taranenko
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
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2025
- Bahasa
- en
- Sumber Database
- arXiv
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- Open Access ✓