A note on the paper arXiv:2207.13335

TL;DR

This paper clarifies that recent purported new permutation polynomials are actually previously known and introduces a new research question in the field.

Contribution

It corrects the record on recent claims of novelty and proposes a new line of inquiry in permutation polynomial research.

Findings

All claimed new permutation polynomials are known.

Clarification of the existing literature on permutation polynomials.

Introduction of a new research question in the area.

Abstract

We show that all of the "new" permutation polynomials in the recent paper arXiv:2207.13335 (H. Song et al.) are in fact known. We also present a new type of question in this area.