Year: 2024
Type: article
Abstract: We study faces of the signed Birkhoff polytopes, denoted by $\Omega_n^{\pm}$. We describe its nonempty faces, $1$-dimensional faces, $2$-dimensional faces, and facets. Moreover, we study the diameter and Hamiltonian connectivity of the graph of $\Omega_n^{\pm}$. In the end, we show that the reduced Gröbner basis of the toric ideal of the signed Birkhoff polytope $\Omega_n^{\pm}$ with respect to the graded reverse lexicographic order induced by rank orders has square-free initial monomials of degree $\leq n$.
Authors: Zhi Chen, Kebin Zhu
Institution: Nanjing Agricultural University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Awards: G1816209773, G4001265025
OpenAlex ID: W4404520247