Eulerian polynomials and polynomial congruences
Kazuki Iijima, Kyouhei Sasaki, Yuuki Takahashi, Masahiko Yoshinaga
TL;DR
This paper investigates polynomial congruences satisfied by Eulerian polynomials and demonstrates that these congruences uniquely characterize the Eulerian polynomial among similar polynomials.
Contribution
The authors establish specific polynomial congruences for Eulerian polynomials and prove these congruences are sufficient to uniquely identify the Eulerian polynomial.
Findings
Eulerian polynomial satisfies particular polynomial congruences.
These congruences are necessary and sufficient for characterizing Eulerian polynomials.
Abstract
We prove that the Eulerian polynomial satisfies certain polynomial congruences. Furthermore, these congruences characterize the Eulerian polynomial.
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