Browsing by Author "Betten, Anton, advisor"

Now showing 1 - 4 of 4

Open Access
Classification algorithms for graphs, digraphs, and linear spaces
(Colorado State University. Libraries, 2007) Al-Azemi, Abdullah, author; Betten, Anton, advisor
Combinatorial incidence structures like graphs, digraphs, and linear spaces are defined modulo an isomorphism relation. Typically we are interested in determining complete systems of representatives of the isomorphism classes, in order to test conjectures or to prove existence or non-existence of examples for new theorems.
Open Access
Classifying simplicial dissections of convex polyhedra with symmetry
(Colorado State University. Libraries, 2021) Mukthineni, Tarun, author; Betten, Anton, advisor; Peterson, Chris, committee member; Rajopadhye, Sanjay, committee member
A convex polyhedron is the convex hull of a finite set ofpoints in R3. A triangulation of a convex polyhedron is a decomposition into a finite number of 3-simplices such that any two intersect in a common face or are disjoint. A simplicial dissection is a decomposition into a finite number of 3-simplices such that no two share an interior point. We present an algorithm to classify the simplicial dissections of a regular polyhedron under the symmetry group of the polyhedron.
Open Access
Imprimitively generated designs
(Colorado State University. Libraries, 2022) Lear, Aaron, author; Betten, Anton, advisor; Adams, Henry, committee member; Nielsen, Aaron, committee member
Designs are a type of combinatorial object which uniformly cover all pairs in a base set V with subsets of V known as blocks. One important class of designs are those generated by a permutation group G acting on V and single initial block b subset of V. The most atomic examples of these designs would be generated by a primitive G. This thesis focuses on the less atomic case where G is imprimitive. Imprimitive permutation groups can be rearranged into a subset of easily understood groups which are derived from G and generate very symmetrical designs. This creates combinatorial restrictions on which group and block combinations can generate a design, turning a question about the existence of combinatorial objects into one more directly involving group theory. Specifically, the existence of imprimitively generated designs turns into a question about the existence of pair orbits of an appropriate size, for smaller permutation groups. This thesis introduces two restrictions on combinations of G and b which can generate designs, and discusses how they could be used to more efficiently enumerate imprimitively generated designs.
Open Access
Two topics in combinatorial optimization: the domino portrait problem and the maximum clique problem
(Colorado State University. Libraries, 2007) Alshamary, Bader, author; Betten, Anton, advisor
Combinatorial Optimization plays a significant role in applied mathematics, supplying solutions to many scientific problems in a variety of fields, including computer science and computational networks. This dissertation first reviews a number of problems from combinatorial optimization and the algorithms used to solve them.