  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.
