We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, Hankel-symmetric, centrosymmetric, and both symmetric and Hankel-symmetric. We determine dimensions of these polytopes and classify their extreme points. We also determine a basis of the real vector spaces generated by permutation matrices with these special structures.
Matrix Permutation matrix Symmetric Hankel-symmetric Centrosymmetric Doubly stochastic Extreme point
Mathematics Subject Classification (2010)
05C50 15B05 15B51 15B48 90C57
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Barnabei, M., Bonetti, F., Silimbani, M.: The Eulerian distribution on centrosymmetric involutions. Discret. Math. Theor. Comput Sci. 11(1), 95–115 (2009)MathSciNetzbMATHGoogle Scholar