W&L Dept. of Mathematics
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According to the 20102011 Washington and Lee University Catalog (undergraduate), all "honors programs require an honors thesis during the senior year, involving six credits (no more, no less) of independent work, such as a significant report based upon field or laboratory research, a creative accomplishment in the arts, or a comparable scholarly undertaking, demonstrating more than simply a mastery of subject matter." This site provides access to honors theses the University Library has included in a digitization project beginning in 2010. In many cases, these records include online access to the complete contents of theses, but, at the authors' wishes, some of these records limit online access to current W&L researchers. For similar reasons, some records allow no online access at all.
This material is made available for use in research, teaching, and private study, pursuant to U.S. Copyright law. The user assumes full responsibility for any use of the materials, including but not limited to, infringement of copyright and publication rights of reproduced materials. Any materials used should be fully credited with the source. Permission for publication of this material, in part or in full, must be secured with the Head of Special Collections and Archives.
Preferred citation: [Identification of item], Student Papers, Record Group 38, Special Collections and Archives, Leyburn Library, Washington and Lee University, Lexington, VA
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Recent Submissions

Realizability of nVertex Graphs with Prescribed Vertex Connectivity, Edge Connectivity, Minimum Degree, and Maximum Degree
This is the fourth and nal thesis that concludes ProfessorWayne M. Dymacek's research project Realizability of nVertex Graphs with Prescribed Vertex Connectivity, Edge Connectivity, Minimum Degree, and Maximum Degree. ... 
Upgrowing Online Linear Discrepancy of Tripleoptimal Partially Ordered Sets
Whether we acknowledge it as a poset or not, posets arise in many natural contexts, and many also seem to warrant linear extensions (or rankings) of the poset. In some sense, the linear discrepancy of a linear extension L ... 
Exploring Extreme Points and Related Properties of Tsirelson Space
Tsirelson space was constructed in 1974 as the first example of a Banach space without an embedded c0 or lp space. In 1989, Casazza and Shura wrote a book Tsirelson's Space devoted to Tsirelson space and its many properties. ... 
Permutation Formula
Runs in permutations and similar topics have been studied by various authors under different names. Hegarty examined permutations of finite abelian groups which avoid what he called progressions. Riordan studied 3runs ... 
Periods of Linearly Recurring Sequences
In this thesis, we investigate sequences defined by linear recurrence relations. These are sequences whose subsequent terms are generated using some linear combination of the previous terms. We call the equation that ... 
Towards an Automated and Customizable Linear Cryptanalysis of SubstitutionPermutation Network Cipher
The increasing scale of the Internet of Things exposes the proprietors and users to a number of security threats in terms of invasion of privacy, identity thefts and the like. It is therefore absolutely necessary that the ... 
Realizability of nVertex Graphs with Prescribed Vertex Connectivity, Edge Connectivity, Minimum Degree, and Maximum Degree
Our work continues a long tradition in graph theory studying the relation ship between vertex connectivity, edge connectivity, and minimum degree. [From Introduction] 
Finding Cycles In The Kth Power Diagraphs Over Integers Modulo A Prime And Over Gaussian Integers Modulo a Gaussian Prime (thesis)
Given Zp where p is an integer prime, let's de ne G(k) p to be the digraph whose set of vertices is Zp such that there is a directed edge from a vertex a to a vertex b if ak b mod p. First, we nd our own way to decide ... 
Arithmetic progressions in permutations (thesis)
In this thesis we will examine progressions in permutations. We will analyze regular and circular permutations with progressions either modular or regular with rise one or two. We will calculate the number of permutations ... 
Steinhaus graphs and pendent vertices (thesis)
Steinhaus graphs have many interesting properties, yet there are many things about them that are not yet known. In [1], a formula was discovered for the total number of Steinhaus graphs on 11 vertices with at least one ...