On the joint distribution of frequences of long $s$-tuples in multinomial scheme with equiprobable events

A sequence of $n$ independent trials (each trial with $k$ equiprobable events) being available, some questions associated with limit distributions of $s$-tuple frequences as $n$, $s\to\infty$, $nk^{-s}\to\lambda\in(0,\infty)$, are considered.