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Jeffrey Beyerl

Publications and source records attributed to Jeffrey Beyerl.

7 recordsLinked to original sources
arXiv2021

Rankin-Cohen brackets of eigenforms and modular forms

We use Maeda's Conjecture to prove that the Rankin-Cohen bracket of an eigenform and any modular form is only an eigenform when forced to be because of the dimensions of the underlying spaces. We further determine when the Rankin-Cohen bracket of an eigenform and modular form is not forced to produce an eigenform and when it is determined by the injectivity of the operator itself. This can also be interpreted as using the Rankin-Cohen bracket operator of eigenforms to create evidence for Maeda's Conjecture.

math.NT↗
arXiv2019

Counting Graph Homomorphisms Involving Complete Graphs

In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have certain desirable properties, called graph homomorphisms, and the probability of such a mapping occurring. By using notions from graph theory and combinatorics, in this paper we prove several new theorems that place bounds on this probability for certain common classes of graphs such as Kn, and show that isolated vertices may safely be ignored.

math.CO↗
arXiv2019

Stability of Critical p-Improper Interval Graphs

A $p$-improper interval graph is an interval graph that has an interval representation in which no interval contains more than $p$ other intervals. A critical $p$-improper interval graph is $p-1$ improper when any vertex is removed. In this paper we investigate the spectrum of impropriety of critical $p$-improper interval graphs upon the removal of a single vertex, which is informally known as the stability of the graph.

math.CO↗
arXiv2011

Interval Graphs with Containment Restrictions

An interval graph is proper iff it has a representation in which no interval contains another. Fred Roberts characterized the proper interval graphs as those containing no induced star $K_{1,3}$. Proskurowski and Telle have studied $q$-proper graphs, which are interval graphs having a representation in which no interval is properly contained in more than $q$ other intervals. Like Roberts they found that their classes of graphs where characterized, each by a single minimal forbidden subgraph. This paper initiates the study of $p$-improper interval graphs where no interval contains more than $p$ other intervals. This paper will focus on a special case of $p$-improper interval graphs for which the minimal forbidden subgraphs are readily described. Even in this case, it is apparent that a very wide variety of minimal forbidden subgraphs are possible.

math.CO↗
arXiv2011

Depth in Bingo Closure

Bingo is played on a $5\times 5$ grid. Take the 25 squares to be the ground set of a closure system in which square $s$ is dependent on a set $S$ of squares iff $s$ completes a line - a row, column, or diagonal - with squares that are already in $S$. The closure of a set $S$ is obtained via an iterative process in which, at each stage, the squares dependent upon the current state are added. In this paper we establish for the $n \times n$ Bingo board the maximum number of steps required in this closure process.

math.CO↗