Loopy, Hankel, and Combinatorially Skew-Hankel Tournaments

We investigate tournaments with a specified score vector having additional structure: loopy tournaments in which loops are allowed, Hankel tournaments which are tournaments symmetric about the Hankel diagonal (the anti-diagonal), and combinatorially skew-Hankel tournaments which are skew-symmetric about the Hankel diagonal. In each case, we obtain necessary and sufficient conditions for existence, algorithms for construction, and switches which allow one to move from any tournament of its type to any other, always staying within the defined type

Symmetric, Hankel-symmetric, and Centrosymmetric Doubly Stochastic Matrices

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