J. Merzel

activity

20212025

collaborators

8 papers

math.CO2025

On divisibility relation graphs

Jonathan L. Merzel, Ján Mináč, Tung T. Nguyen +1

For each positive integer $n$ , we define the divisibility relation graph $D_{n}$ whose vertex set is the set of divisors of $n$ , and in which two vertices are adjacent if one is a di…

math.CO2024

Paint cost spectrum of perfect $k$ -ary trees

Sonwabile Mafunda, Jonathan L. Merzel, K. E. Perry +1

We determine the paint cost spectrum for perfect $k$ -ary trees. A coloring of the vertices of a graph $G$ with $d$ colors is said to be \emph{ $d$ -distinguishing} if only the trivia…

math.RA2023

On the arithmetic of the join rings over finite fields

Sunil K. Chebolu, Jonathan Merzel, Ján Mináč +3

Given a collection ${G_{i}}_{i = 1}^{d}$ of finite groups and a ring $R$ , we have previously introduced and studied certain foundational properties of the join ring $\mathcal{J}_{G_1,…

math.SP2023

Spectral perturbation by rank- $m$ matrices

Jonathan L. Merzel, Ján Mináč, Tung T. Nguyen +1

Let $A$ and $B$ designate $n \times n$ matrices with coefficients in a field $F$ . In this paper, we completely answer the following question: For $A$ fixed, what are the possible ch…

math.RT2023

$G$ -circulant Matrices and the Classical Maschke Theorem

Jon Merzel

In this note, we use the isomorphism of the ring of $G$ -circulant matrices over a field $k$ with the group ring $k [G]$ to derive a very short proof of the Classical Maschke Theorem…

math.RA2022

On the joins of group rings

Sunil K. Chebolu, Jonathan L. Merzel, Ján Mináč +4

Given a collection ${G_{i}}_{i = 1}^{d}$ of finite groups and a ring $R$ , we define a subring of the ring $M_{n} (R)$ ( $n = \sum_{i = 1}^{d} ∣ G_{i} ∣)$ that encompasses all the individual group…

math.SP2021

Spectral perturbation by rank one matrices

Jon Merzel, Jan Minac, Lyle Muller +2

Let $A$ be a matrix of size $n \times n$ over an algebraically closed field $F$ and $q (t)$ a monic polynomial of degree $n$ . In this article, we describe the necessary and sufficie…

math.NT2021

A Linear Division-Based Recursion with Number Theoretic Applications

Jonathan L. Merzel

A simple remark on infinite series is presented. This applies to a particular recursion scenario, which in turn has applications related to a classical theorem on Euler's phi-funct…