The empty set is an $n$-ary relation for every $n$, right?
How should we call a pair $(n;r)$ consisting of some number $n$ and an $n$-ary relation $r$?
To specify $n$ is necessary only when $r$ is empty, but because there are no reason for $r$ not to be empty, I need to specify $n$ explicitly.
Any term describing this situation?