The call type( expr, 'permlist' ) returns true if expr is a permutation of the integers $\{1,2,...,n\}$, where $n=\mathrm{nops}\left(\mathrm{expr}\right)$, and returns false otherwise.

A permutation of $\{1,2,...,n\}$ is a list whose members are exactly these integer, in which each integer occurs exactly once.

$\mathrm{type}\left(\left\{1\,2\,3\right\}\,'\mathrm{permlist}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\left[1\,2\,3\right]\,'\mathrm{permlist}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\left[2\,1\,3\right]\,'\mathrm{permlist}'\right)$

$\mathrm{true}$

$\mathrm{type}\left(\left[2\,1\,2\right]\,'\mathrm{permlist}'\right)$

$\mathrm{false}$

$\mathrm{type}\left(\left[\left[1\,2\right]\,\left[3\,4\right]\right]\,'\mathrm{permlist}'\right)$

$\mathrm{false}$