The Determining Number and Cost of 2-Distinguishing of Select Kneser Graphs
A graph $G$ is said to be \emph{d-distinguishable} if there exists a not-necessarily proper coloring with $d$ colors such that only the trivial automorphism preserves the color classes. For a...
View ArticleStrong Recovery In Group Synchronization
The group synchronization problem is to estimate unknown group elements at the vertices of a graph when given a set of possibly noisy observations of group differences at the edges. We consider the...
View ArticleOptimal Monohedral Tilings of Hyperbolic Surfaces
The hexagon is the least-perimeter tile in the Euclidean plane for any given area. On hyperbolic surfaces, this "isoperimetric" problem differs for every given area, as solutions do not scale. Cox...
View ArticleA Note On The Involutive Concordance Invariants For Certain (1,1)-Knots
A knot K is a smooth embedding of the circle into the three-dimensional sphere; two knots are said to be concordant if they form the boundary of an annulus properly embedded into the product of the...
View ArticleConstructing Spanning Sets of Affine Algebraic Curvature Tensors
In this paper, we construct two spanning sets for the affine algebraic curvature tensors. We then prove that every 2-dimensional affine algebraic curvature tensor can be represented by a single...
View ArticleMotion Planning Algorithm in a Y-Graph
We present an explicit algorithm for two robots to move autonomously and without collisions on a track shaped like the letter Y. Configuration spaces are of practical relevance in designing safe...
View ArticleSome Thoughts on The 3 × 3 Magic Square of Squares Problem
A magic square is a square grid of numbers where each row, column, and long diagonal has the same sum (called the magic sum). An open problem popularized by Martin Gardner asks whether there exists a...
View ArticleA Characterization of Complex-Valued Random Variables With...
A complex-valued random variable Z is rotationally invariant if the moments of Z are the same as the moments of W=e^{i*theta}Z. In the first part of the article, we characterize such random variables,...
View ArticleThe Existence of Solutions to a System of Nonhomogeneous Difference Equations
This article will demonstrate a process using Fixed Point Theory to determine the existence of multiple positive solutions for a type of system of nonhomogeneous even ordered boundary value problems...
View ArticleOn Solutions of First Order PDE with Two-Dimensional Dirac Delta Forcing Terms
We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by...
View ArticleThe Mean Sum of Squared Linking Numbers of Random Piecewise-Linear Embeddings...
DNA and other polymer chains in confined spaces behave like closed loops. Arsuaga et al. \cite{AB} introduced the uniform random polygon model in order to better understand such loops in confined...
View ArticleNumber of Regions Created by Random Chords in the Circle
In this paper we discuss the number of regions in a unit circle after drawing n i.i.d. random chords in the circle according to a particular family of distribution. We find that as n goes to infinity,...
View ArticleUtilizing graph thickness heuristics on the Earth-moon Problem
This paper utilizes heuristic algorithms for determining graph thickness in order to attempt to find a 10-chromatic thickness-2 graph. Doing so would eliminate 9 colors as a potential solution to the...
View Articlek-Distinct Lattice Paths
Lattice paths can be used to model scheduling and routing problems, and, therefore, identifying maximum sets of k-distinct paths is of general interest. We extend the work previously done by Gillman...
View ArticleA Model for the Multi-Virus Contact Process
We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability...
View ArticleStructure of a Total Independent Set
Let $G$ be a simple, connected and finite graph with order $n$. Denote the independence number, edge independence number and total independence number by $\alpha(G), \alpha'(G)$ and $\alpha''(G)$...
View ArticleElliptic triangles which are congruent to their polar triangles
We prove that an elliptic triangle is congruent to its polar triangle if and only if six specific Wallace-Simson lines of the triangle are concurrent. (If a point projected onto a triangle has the...
View ArticleDivisibility Probabilities for Products of Randomly Chosen Integers
We find a formula for the probability that the product of n positive integers, chosen at random, is divisible by some integer d. We do this via an inductive application of the Chinese Remainder...
View ArticleFurther Generalizations of Happy Numbers
A positive integer n is defined to be happy if iteration of the function taking the sum of the squares of the digits of n eventually reaches 1. In this paper we generalize the concept of happy numbers...
View ArticleEigenvalue Algorithm for Hausdorff Dimension on Complex Kleinian Groups
In this manuscript, we present computational results approximating the Hausdorff dimension for the limit sets of complex Kleinian groups. We apply McMullen's eigenvalue algorithm \cite{mcmullen} in...
View Article
