Louisiana Tech University
Boise State University
Monmouth University
Baldwin Wallace University, Berea
James Madison University
University of Mary Washington
California State University, San Bernardino
Duquesne University
Facets Of The Union-Closed Polytope,
2023
University of Massachusetts Amherst
Facets Of The Union-Closed Polytope, Daniel Gallagher
Doctoral Dissertations
In the haze of the 1970s, a conjecture was born to unknown parentage...the union-closed sets conjecture. Given a family of sets $\FF$, we say that $\FF$ is union-closed if for every two sets $S, T \in \FF$, we have $S \cup T \in \FF$. The union-closed sets conjecture states that there is an element in at least half of the sets of any (non-empty) union-closed family. In 2016, Pulaj, Raymond, and Theis reinterpreted the conjecture as an optimization problem that could be formulated as an integer program. This thesis is concerned with the study of the polytope formed by taking …
Msis-Kadelka: On The Uniqueness Of Network Identification,
2023
University of Dayton
Msis-Kadelka: On The Uniqueness Of Network Identification, Alan Veliz-Cuba, Elena Dimitrova
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Msis-Kadelka: Algebraic Methods For Inferring Discrete Models Of Biological Networks,
2023
Southern Methodist University
Msis-Kadelka: Algebraic Methods For Inferring Discrete Models Of Biological Networks, Brandilyn Stigler
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Divisibility Probabilities For Products Of Randomly Chosen Integers,
2023
University of Maryland
Divisibility Probabilities For Products Of Randomly Chosen Integers, Noah Y. Fine
Rose-Hulman Undergraduate Mathematics Journal
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 Theorem, generating functions, and several other combinatorial arguments. Additionally, we apply this formula to find a unique, but slow, probabilistic primality test.
Structure Of A Total Independent Set,
2023
University of Southampton
Structure Of A Total Independent Set, Lewis Stanton
Rose-Hulman Undergraduate Mathematics Journal
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 $\alpha''(G)$ respectively. This paper establishes an upper bound for $\alpha''(G)$ in terms of $\alpha(G)$, $\alpha'(G)$ and $n$. We also describe the possible structures for a total independent set containing a given number of elements.
K-Distinct Lattice Paths,
2023
Valparaiso University
K-Distinct Lattice Paths, Eric J. Yager, Marcus Engstrom
Rose-Hulman Undergraduate Mathematics Journal
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 et. al. to determine the order of a maximum set of k-distinct lattice paths. In particular, we disprove a conjecture by Gillman that a greedy algorithm gives this maximum order and also refine an upper bound given by Brewer et. al. We illustrate that brute force is an inefficient method to determine the maximum order, as it has time complexity O(nk).
Utilizing Graph Thickness Heuristics On The Earth-Moon Problem,
2023
York College of Pennsylvania
Utilizing Graph Thickness Heuristics On The Earth-Moon Problem, Robert C. Weaver
Rose-Hulman Undergraduate Mathematics Journal
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 Earth-moon Problem. An empirical analysis of the algorithms made by the author are provided. Additionally, the paper lists various graphs that may or nearly have a thickness of 2, which may be solutions if one can find two planar subgraphs that partition all of the graph’s edges.
On Nowhere Zero 4-Flows In Regular Matroids,
2023
Indiana University Northwest
On Nowhere Zero 4-Flows In Regular Matroids, Xiaofeng Wang, Taoye Zhang, Ju Zhou
Theory and Applications of Graphs
Walton and Welsh proved that if a co-loopless regular matroid M does not have a minor in {M(K(3,3)),M∗(K5)}, then M admits a nowhere zero 4-flow. Lai, Li and Poon proved that if M does not have a minor in {M(K5),M∗(K5)}, then M admits a nowhere zero 4-flow. We prove that if a co-loopless regular matroid M does not have a minor in {M((P10)¯3 ),M∗(K5)}, then M admits a nowhere zero 4-flow where (P10)¯3 is the graph obtained from the Petersen graph P10by contracting 3 edges of a perfect matching. As …
The Mean Sum Of Squared Linking Numbers Of Random Piecewise-Linear Embeddings Of $K_N$,
2023
University of Notre Dame
The Mean Sum Of Squared Linking Numbers Of Random Piecewise-Linear Embeddings Of $K_N$, Yasmin Aguillon, Xingyu Cheng, Spencer Eddins, Pedro Morales
Rose-Hulman Undergraduate Mathematics Journal
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 spaces using probabilistic and knot theoretical techniques, giving some classification on the mean squared linking number of such loops. Flapan and Kozai \cite{flapan2016linking} extended these techniques to find the mean sum of squared linking numbers for random linear embeddings of complete graphs $K_n$ and found it to have order $\Theta(n(n!))$. We further these ideas by inspecting random piecewise-linear embeddings of complete graphs and give introductory-level summaries of the ideas …
Fuglede's Conjecture In Some Finite Abelian Groups,
2023
The Graduate Center, City University of New York
Fuglede's Conjecture In Some Finite Abelian Groups, Thomas Fallon
Dissertations, Theses, and Capstone Projects
This dissertation thoroughly examines Fuglede's Conjecture within some discrete settings, shedding light on its intricate details. Fuglede's Conjecture establishes a profound connection between the geometric property of being a tiling set and the analytical attribute of being a spectral set. By exploring the conjecture on various discrete settings, this thesis delves into the implications and ramifications of the conjecture, unraveling its implications within the field.
Reversibility Of Stranded Cellular Automata,
2023
Rose-Hulman Institute of Technology
Reversibility Of Stranded Cellular Automata, Allyn Loyd
Mathematical Sciences Technical Reports (MSTR)
Cellular automata, such as the Stranded Cellular Automaton (SCA) model created by Joshua and Lana Holden, can be used to model weaving patterns. Similar models can be constructed to model macrame patterns, where strands are knotted together. If a rule is injective, then it is reversible. If a rule is surjective, then every configuration has at least one predecessor. In this paper, we will discuss the injectivity and surjectivity of several new SCA models in order to find reversible rules. We will also analyze the number of configurations with no predecessors and the number of configurations that map to the …
On The Order-Type Complexity Of Words, And Greedy Sidon Sets For Linear Forms,
2023
The Graduate Center, City University of New York
On The Order-Type Complexity Of Words, And Greedy Sidon Sets For Linear Forms, Yin Choi Cheng
Dissertations, Theses, and Capstone Projects
This work consists of two parts. In the first part, we study the order-type complexity of right-infinite words over a finite alphabet, which is defined to be the order types of the set of shifts of said words in lexicographical order. The set of shifts of any aperiodic morphic words whose first letter in the purely-morphic pre-image occurs at least twice in the pre-image has the same order type as Q ∩ (0, 1), Q ∩ (0, 1], or Q ∩ [0, 1). This includes all aperiodic purely-morphic binary words. The order types of uniform-morphic ternary words were also studied, …
An Analysis Of The Sequence Xn+2 = I M Xn+1 + Xn,
2023
Coastal Carolina University
An Analysis Of The Sequence Xn+2 = I M Xn+1 + Xn, David Duncan, Prashant Sansgiry, Ogul Arslan, Jensen Meade
Journal of the South Carolina Academy of Science
We analyze the sequence Xn+2 = imXn+1 + Xn, with X1 = X2 = 1 + i, where i is the imaginary number and m is a real number. Plotting the sequence in the complex plane for different values of m, we see interesting figures from the conic sections. For values of m in the interval (−2, 2) we show that the figures generated are ellipses. We also provide analysis which prove that for certain values of m, the sequence generated is periodic with even period.
The Gamma-Signless Laplacian Adjacency Matrix Of Mixed Graphs,
2023
College of Engineering and Technology, American University of the Middle East, Kuwait
The Gamma-Signless Laplacian Adjacency Matrix Of Mixed Graphs, Omar Alomari, Mohammad Abudayah, Manal Ghanem
Theory and Applications of Graphs
The α-Hermitian adjacency matrix Hα of a mixed graph X has been recently introduced. It is a generalization of the adjacency matrix of unoriented graphs. In this paper, we consider a special case of the complex number α. This enables us to define an incidence matrix of mixed graphs. Consequently, we define a generalization of line graphs as well as a generalization of the signless Laplacian adjacency matrix of graphs. We then study the spectral properties of the gamma-signless Laplacian adjacency matrix of a mixed graph. Lastly, we characterize when the signless Laplacian adjacency matrix of …
Generating Polynomials Of Exponential Random Graphs,
2023
The University of Western Ontario
Generating Polynomials Of Exponential Random Graphs, Mohabat Tarkeshian
Electronic Thesis and Dissertation Repository
The theory of random graphs describes the interplay between probability and graph theory: it is the study of the stochastic process by which graphs form and evolve. In 1959, Erdős and Rényi defined the foundational model of random graphs on n vertices, denoted G(n, p) ([ER84]). Subsequently, Frank and Strauss (1986) added a Markov twist to this story by describing a topological structure on random graphs that encodes dependencies between local pairs of vertices ([FS86]). The general model that describes this framework is called the exponential random graph model (ERGM).
In the past, determining when a probability distribution has strong …
Dna Self-Assembly Of Trapezohedral Graphs,
2023
California State University - San Bernardino
Dna Self-Assembly Of Trapezohedral Graphs, Hytham Abdelkarim
Electronic Theses, Projects, and Dissertations
Self-assembly is the process of a collection of components combining to form an organized structure without external direction. DNA self-assembly uses multi-armed DNA molecules as the component building blocks. It is desirable to minimize the material used and to minimize genetic waste in the assembly process. We will be using graph theory as a tool to find optimal solutions to problems in DNA self-assembly. The goal of this research is to develop a method or algorithm that will produce optimal tile sets which will self-assemble into a target DNA complex. We will minimize the number of tile and bond-edge types …
One Formula For Non-Prime Numbers: Motivations And Characteristics,
2023
Department of Basic Science, Faculty of Engineering, The British University in Egypt
One Formula For Non-Prime Numbers: Motivations And Characteristics, Mahmoud Mansour, Kamal Hassan Prof.
Basic Science Engineering
Primes are essential for computer encryption and cryptography, as they are fundamental units of whole numbers and are of the highest importance due to their mathematical qualities. However, identifying a pattern of primes is not easy. Thinking in a different way may get benefits, by considering the opposite side of the problem which means focusing on non-prime numbers. Recently, researchers introduced, the pattern of non-primes in two maximal sets while in this paper, non-primes are presented in one formula. Getting one-way formula for non-primes may pave the way for further applications based on the idea of primes.
Waste Treatment Facility Location For Hotel Chains,
2023
Universidad de Las Palmas de Gran Canaria
Waste Treatment Facility Location For Hotel Chains, Dolores R. Santos-Peñate, Rafael R. Suárez-Vega, Carmen Florido De La Nuez
ITSA 2022 Gran Canaria - 9th Biennial Conference: Corporate Entrepreneurship and Global Tourism Strategies After Covid 19
Tourism generates huge amounts of waste. About half of the waste generated by hotels is food and garden bio-waste. This bio-waste can be used to make compost and pellets. In turn, pellets can be used as an absorbent material in composters and as an energy source. We consider the problem of locating composting and pellet-making facilities so that the bio-waste generated by a chain of hotels can be managed at or close to the generation points. An optimization model is applied to locate the facilities and allocate the waste and products, and several scenarios are analysed. The study shows that, …
A Bit-Parallel Tabu Search Algorithm For Finding Es2 -Optimal And Minimax-Optimal Supersaturated Designs,
2023
Universidad Nacional Autónoma de México
A Bit-Parallel Tabu Search Algorithm For Finding Es2 -Optimal And Minimax-Optimal Supersaturated Designs, Luis B. Morales, Dursun A. Bulotuglu
Faculty Publications
We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, smax=4t+i, where i ∈ {0,2}, t ∈ Z≥0 and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most (N+4t+i)/4 points. Using this equivalence, we formulate the search for two-symbol E(s2)-optimal and minimax-optimal SSDs with smax ∈ {2,4,6} as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found E(s2)-optimal and minimax-optimal SSDs achieving the sharpest known E(s2) lower bound with …
A Pebbling Game On Powers Of Paths,
2023
Lehigh University
A Pebbling Game On Powers Of Paths, Garth Isaak, Matthew Prudente, Joseph M. Marcinik Iii
Communications on Number Theory and Combinatorial Theory
Two Player Graph Pebbling is an extension of graph pebbling. Players Mover and Defender use pebbling moves, the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex, to win. If a specified vertex has a pebble on it, then Mover wins. If a specified vertex is pebble-free and there are no more valid pebbling moves, then Defender wins. The Two-Player Pebbling Number of a graph G, η(G), is the minimum m such that for every arrangement of m pebbles and for any specified vertex, Mover can win. We specify the …
