The elements in the group of centrosymmetric n×n permutation matrices are the extreme points of a convex subset of n2-dimensional Euclidean space, which we characterize by a very simple set of linear inequalities, thereby providing an interesting solvable case of a difficult problem posed by L. Mirsky, as well as a new analogue of the famous theorem on doubly stochastic matrices due to G. Birkhoff. Several further theorems of a related nature also are included. © 1977.
Cruse, A. B. (1977). Some combinatorial properties of centrosymmetric matrices. Linear Algebra and Its Applications, 16(1), 65–77. https://doi.org/10.1016/0024-3795(77)90020-9