arXiv subjects

Kimiko Hasegawa

Publications and source records attributed to Kimiko Hasegawa.

2 recordsLinked to original sources

arXiv2026

Division properties of commuting polynomials

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.

math.AC↗

arXiv2024

Weighted sums of rooted spanning forests on cycles with pendant edges

We derive two formulas for the weighted sums of rooted spanning forests of particular sequence of graphs by using the matrix tree theorem. We consider cycle graphs with edges so called the pendant edges. One of our formula can be described as a variable transformation of the Chebyshev polynomial. They have particular algebraic properties.

math.CO↗