Division properties of commuting polynomials
Commutative Algebra
2026-03-05 v2 Combinatorics
Abstract
Polynomials commute under composition are referred to as commuting polynomials. In this paper, we study division properties for commuting polynomials with rational (and integer) coefficients. As a consequence, we show an algebraic particularity of the commuting polynomials coming from weighted sums for cycle graphs with pendant edges (arXiv:2402.07209v1.). We also discuss a set of commuting polynomials over a field of positive characteristic.
Cite
@article{arxiv.2404.01605,
title = {Division properties of commuting polynomials},
author = {Kimiko Hasegawa and Rin Sugiyama},
journal= {arXiv preprint arXiv:2404.01605},
year = {2026}
}
Comments
20 pages, Added a discussion in case where the base field is positive characteristic