On a polynomial congruence for Eulerian polynomials

TL;DR

This paper presents a concise proof of a polynomial congruence related to Eulerian polynomials, utilizing generating functions, and builds on previous work involving hyperplane arrangements and roots of unity.

Contribution

It offers a new, simplified proof of a known polynomial congruence for Eulerian polynomials using generating functions.

Findings

Provides a short proof of the polynomial congruence

Connects generating functions with hyperplane arrangements and roots of unity

Simplifies previous proofs of the congruence

Abstract

We give a short proof, using generating functions, for a polynomial congruence for Eulerian polynomials first proved, using arrangements of hyperplanes, by Yoshinaga and later proved, using roots of unity, by Iijima, Sasaki, Takahashi, and Yoshinaga.