Fix type errors in permutations (#9007)

* updating DIRECTORY.md

* types(permuations): Rename permute2

* Apply suggestions from code review

Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

* fix(permutations): Call permute_recursive

* fix(permutations): Correct permutations order

---------

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>