When one says "a random permutation of $[n]$" what does "$[n]$" refer to? Here, $n \in \mathbb{N}\backslash\{0\}$.
Also, what does a "$c\sqrt{n}$-tuple $S = (s_1, s_2, ..., s_{c\sqrt{n}})$ of elements of $[n]$ mean? As far as I know, the number of elements in a tuple is a positive integer.
