This is a follow-up to an earlier question.
Suppose you start at a given score sequence, and ask "how many tournaments, up to isomorphism, have this score sequence?" For $\{0, 1, 2, ..., n-1\}$ the answer is $1$, and for a few other sequences.
If we set aside the transitive tournaments for a moment, one can ask are these other sequences (for whom the answer is $1$)?
According to the theorem that tournaments are made up of a transitive string of strong components, we are looking for strong tournaments such that no other tournament exists having the same degree sequence.
The only examples seem to be the regular tournaments ($\{0\}, \{1, 1, 1\}, \{2, 2, 2, 2, 2\}$ etc.). And also $\{1, 1, 2, 2\}$. Are these the only ones? What others are there?
Thanks