There are a lot of papers on degree/score sequences of tournaments, starting on a given sequence, and constructing a tournament that has that degree sequence, and so forth.
But what if 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, are these other sequences (for whom the answer is 1) simply miscellaneous? It seems as the sequences get longer the number of possible tournaments grows, so is it the case that these "miscellaneous" sequences eventually stop?
Or is there some nontrivial infinite class that I am not noticing?
I suppose one could ask about connected digraphs too, not only tournaments.