Cedar Crest College

output

20182025

most citedMonogenic Quartic Polynomials and Their Galois Groups

6 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

collaborating institutions

14 papers

math.NT2025

A further investigation on covering systems with odd moduli

Chris Bispels, Matthew Cohen, Joshua Harrington +4

Erdős first introduced the idea of covering systems in 1950. Since then, much of the work in this area has concentrated on identifying covering systems that meet specific condition…

math.GT2025

Constructions of and Bounds on the Toric Mosaic Number

Kendall Heiney, Margaret Kipe, Samantha Pezzimenti +2

Knot mosaics were introduced by Kauffman and Lomonaco in the context of quantum knots, but have since been studied for their own right. A classical knot mosaic is formed on a squar…

math.NT2024★ 6 cited

Monogenic Quartic Polynomials and Their Galois Groups

Joshua Harrington, Lenny Jones

A monic polynomial $f (x) \in Z [x]$ of degree $N$ is called monogenic if $f (x)$ is irreducible over $Q$ and ${1, θ, θ^{2}, \dots, θ^{N - 1}}$ is a basis for the ring…

math.CO2024★ 1 cited

Paired $(n - 1)$ -to- $(n - 1)$ disjoint path covers in bipartite transposition-like graphs

Anna Coleman, Gabrielle Fischberg, Charles Gong +2

A paired $k$ -to- $k$ disjoint path cover of a graph $G$ is a collection of pairwise disjoint path subgraphs $P_{1}, P_{2}, \dots, P_{k}$ such that each $P_{i}$ has prescribed vertices $s_{i}$ a…

math.NT2023

Arithmetic progressions of integers that are relatively prime to their digital sums

Ryan Blau, Joshua Harrington, Sarah Lohrey +2

For an integer $b \geq 2$ , we call a positive integer $b$ -anti-Niven if it is relatively prime to the sum of the digits in its base- $b$ representation. In this article, we investiga…

math.NT2023★ 2 cited

Every arithmetic progression contains infinitely many $b$ -Niven numbers

Joshua Harrington, Matthew Litman, Tony W. H. Wong

For an integer $b \geq 2$ , a positive integer is called a $b$ -Niven number if it is a multiple of the sum of the digits in its base- $b$ representation. In this article, we show that…

math.CO2022

Probabilistic chip-collecting games with modulo winning conditions

Joshua Harrington, Xuwen Hua, Xufei Liu +3

Let $a$ , $b$ , and $n$ be integers with $0 < a < b < n$ . In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects $a$ chips or $b$ …

math.CO2021

Distance in Latin Squares

Omar Aceval, Paige Beidelman, Jieqi Di +4

A Latin square of order $n$ is an $n \times n$ array which contains $n$ distinct symbols exactly once in each row and column. We define the adjacent distance between two adjacent ce…

math.NT2021★ 1 cited

Covering systems with odd moduli

Joshua Harrington, Yewen Sun, Wing Hong Tony Wong

The concept of a covering system was first introduced by Erdős in 1950. Since their introduction, a lot of the research regarding covering systems has focused on the existence of c…

math.NT2021

Residue sums of Dickson polynomials over finite fields

Thomas Brazelton, Joshua Harrington, Matthew Litman +1

Given a polynomial with integral coefficients, one can inquire about the possible residues it can take in its image modulo a prime $p$ . The sum over the distinct residues can somet…

math.NT2020

On the properties of fibotomic polynomials

Cameron Byer, Tyler Dvorachek, Emily Eckard +3

Define the $n$ -th fibotomic polynomial to be the product of the monic irredicible factors of the $n$ -th Fibonacci polynomial which are not factors of any Fibonacci polynomial of sm…

math.CO2020★ 6 cited

Sum index and difference index of graphs

Joshua Harrington, Eugene Henninger-Voss, Kedjar Karhadkar +2

Let $G$ be a nonempty simple graph with a vertex set $V (G)$ and an edge set $E (G)$ . For every injective vertex labeling $f : V (G) \to Z$ , there are two induced edge labelings,…

math.NT2018★ 1 cited

An Investigation on Partitions with Equal Products

Byungchul Cha, Adam Claman, Joshua Harrington +6

An ordered triple $(s, p, n)$ is called admissible if there exist two different multisets $X = {x_{1}, x_{2}, \dots, x_{n}}$ and $Y = {y_{1}, y_{2}, \dots, y_{n}}$ such that $X$ and $Y$ share the sa…

math.CO2018★ 1 cited

On the Domination Number of Permutation Graphs and an Application to Strong Fixed Points

Theresa Baren, Michael Cory, Mia Friedberg +6

A permutation graph $G_{π}$ is a simple graph with vertices corresponding to the elements of $π$ and an edge between $i$ and $j$ when $i$ and $j$ are inverted in $π$ . A set of vertic…