## ASU Electronic Theses and Dissertations

This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.

In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.

Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.

- Fishel, Susanna
- 17 Arizona State University
- 12 Czygrinow, Andrzej
- 8 Jones, John
- 7 Childress, Nancy
- 7 Colbourn, Charles
- 5 Bremner, Andrew
- more
- 5 Hurlbert, Glenn
- 5 Kierstead, Henry
- 4 Spielberg, John
- 3 Kierstead, Henry A
- 3 Paupert, Julien
- 1 AL-SULEIMAN, SULTAN
- 1 Carrillo, Benjamin
- 1 Debiasio, Louis
- 1 Elledge, Shawn Michael
- 1 Horan, Victoria E.
- 1 Hurlbert, Glenn H
- 1 Kadell, Kevin
- 1 Kaliszewski, Steven
- 1 Kamat, Vikram Mahendra
- 1 Kawski, Matthias
- 1 Kierstead, Hal A
- 1 Kim, Younghwan
- 1 Kotschwar, Brett
- 1 Molla, Theodore
- 1 Nelson, Luke Edwin
- 1 Nguyen, Tho Xuan
- 1 Oursler, Roy
- 1 Quigg, John
- 1 Rabern, Landon
- 1 Sen, Arunabha
- 1 Smith, Matthew Earl
- 1 Spielberg, Jack
- 1 Treat, Kevin
- 1 Wells, Joseph
- 1 Yie, Jangwon
- 1 Zinzer, Scott

- 17 English

- 17 Public

- Mathematics
- 2 Maximal Chains
- 2 Tamari Lattices
- 2 Theoretical mathematics
- 1 $\lambda$-invariant
- 1 Borodin-Kostochka
- 1 Brooks
- more
- 1 Cambrian Lattices
- 1 Catalan lattice
- 1 Circular arc graph
- 1 Combinatorics
- 1 Degree
- 1 Diophantine equations
- 1 Directed Graphs
- 1 Enumeration
- 1 Extremal Graph Theory
- 1 First-Fit
- 1 Gamma-transform
- 1 Graph
- 1 Graph Theory
- 1 Gray codes
- 1 Higher Stasheff-Tamari order
- 1 Hypergraph
- 1 Iwasawa Invariant
- 1 Iwasawa Theory
- 1 Iwasawa theory 11R23
- 1 Lattices
- 1 Limits
- 1 Loose Cycle
- 1 On-line chain partition
- 1 On-line graph coloring
- 1 Partially ordered set
- 1 Pseudo-polynomial
- 1 Rainbow Cycle
- 1 Ramsey Number
- 1 Tamari lattice
- 1 Tiling
- 1 Tree
- 1 Turan Number
- 1 affine permutation
- 1 algebraic number theory
- 1 cd-index
- 1 chordal graphs
- 1 chvatal's conjecture
- 1 clique
- 1 coloring
- 1 complex hyperbolic gometry
- 1 cross-intersecting families
- 1 cyclic sieving phenomenon
- 1 discrete groups
- 1 elliptic curve
- 1 elliptic curve Chabauty
- 1 flag enumeration
- 1 independent sets
- 1 intersecting families
- 1 lattices
- 1 m-eralized Cambrian Lattices
- 1 matchings
- 1 maximum degree
- 1 non-arithmetic
- 1 number theory
- 1 overlap cycles
- 1 p-adic Valued Measure
- 1 p-adic analysis
- 1 profinite groups 20E18
- 1 stability analysis
- 1 the uncrossing partial order
- 1 universal cycles

- Microfluidic Models of Tumor-Stroma Interactions to Study the Interplay of Cancer Cells with their Surrounding Microenvironment
- Ain't She Sweet: A Critical Choreographic Study of Identity & Intersectionality
- Suppositions for Desert Modernism: An Architectural Framework Informed by Climate, Natural Light, and Topography
- Concurrent reduction of trichloroethylene and perchlorate in continuous flow-through soil columns
- Design and Fabrication of Fabric ReinforcedTextile Actuators forSoft Robotic Graspers

Every graph can be colored with one more color than its maximum degree. A well-known theorem of Brooks gives the precise conditions under which a graph can be colored with maximum degree colors. It is natural to ask for the required conditions on a graph to color with one less color than the maximum degree; in 1977 Borodin and Kostochka conjectured a solution for graphs with maximum degree at least 9: as long as the graph doesn't contain a maximum-degree-sized clique, it can be colored with one fewer than the maximum degree colors. This study attacks the conjecture on multiple ...

- Contributors
- Rabern, Landon, Kierstead, Henry, Colbourn, Charles, et al.
- Created Date
- 2013

The primary focus of this dissertation lies in extremal combinatorics, in particular intersection theorems in finite set theory. A seminal result in the area is the theorem of Erdos, Ko and Rado which finds the upper bound on the size of an intersecting family of subsets of an n-element set and characterizes the structure of families which attain this upper bound. A major portion of this dissertation focuses on a recent generalization of the Erdos--Ko--Rado theorem which considers intersecting families of independent sets in graphs. An intersection theorem is proved for a large class of graphs, namely chordal graphs which ...

- Contributors
- Kamat, Vikram Mahendra, Hurlbert, Glenn, Colbourn, Charles, et al.
- Created Date
- 2011

In the 1980's, Gromov and Piatetski-Shapiro introduced a technique called "hybridization'' which allowed them to produce non-arithmetic hyperbolic lattices from two non-commensurable arithmetic lattices. It has been asked whether an analogous hybridization technique exists for complex hyperbolic lattices, because certain geometric obstructions make it unclear how to adapt this technique. This thesis explores one possible construction (originally due to Hunt) in depth and uses it to produce arithmetic lattices, non-arithmetic lattices, and thin subgroups in SU(2,1). Dissertation/Thesis

- Contributors
- Wells, Joseph, Paupert, Julien, Kotschwar, Brett, et al.
- Created Date
- 2019

Gray codes are perhaps the best known structures for listing sequences of combinatorial objects, such as binary strings. Simply defined as a minimal change listing, Gray codes vary greatly both in structure and in the types of objects that they list. More specific types of Gray codes are universal cycles and overlap sequences. Universal cycles are Gray codes on a set of strings of length n in which the first n-1 letters of one object are the same as the last n-1 letters of its predecessor in the listing. Overlap sequences allow this overlap to vary between 1 and n-1. ...

- Contributors
- Horan, Victoria E., Hurlbert, Glenn H, Czygrinow, Andrzej, et al.
- Created Date
- 2012

The Tamari lattice T(n) was originally defined on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Since then it has been studied in various areas of mathematics including cluster algebras, discrete geometry, algebraic combinatorics, and Catalan theory. Although in several related lattices the number of maximal chains is known, the enumeration of these chains in Tamari lattices is still an open problem. This dissertation defines a partially-ordered set on equivalence classes of certain saturated chains of T(n) called the Tamari Block poset, TB(lambda). It further proves TB(lambda) is a ...

- Contributors
- Treat, Kevin, Fishel, Susanna, Czygrinow, Andrzej, et al.
- Created Date
- 2016

This dissertation will cover two topics. For the first, let $K$ be a number field. A $K$-derived polynomial $f(x) \in K[x]$ is a polynomial that factors into linear factors over $K$, as do all of its derivatives. Such a polynomial is said to be {\it proper} if its roots are distinct. An unresolved question in the literature is whether or not there exists a proper $\Q$-derived polynomial of degree 4. Some examples are known of proper $K$-derived quartics for a quadratic number field $K$, although other than $\Q(\sqrt{3})$, these fields have quite large discriminant. (The second known field is $\Q(\sqrt{3441})$.) ...

- Contributors
- Carrillo, Benjamin, Jones, John, Bremner, Andrew, et al.
- Created Date
- 2019

In 1959, Iwasawa proved that the size of the $p$-part of the class groups of a $\mathbb{Z}_p$-extension grows as a power of $p$ with exponent ${\mu}p^m+{\lambda}\,m+\nu$ for $m$ sufficiently large. Broadly, I construct conditions to verify if a given $m$ is indeed sufficiently large. More precisely, let $CG_m^i$ (class group) be the $\epsilon_i$-eigenspace component of the $p$-Sylow subgroup of the class group of the field at the $m$-th level in a $\mathbb{Z}_p$-extension; and let $IACG^i_m$ (Iwasawa analytic class group) be ${\mathbb{Z}_p[[T]]/((1+T)^{p^m}-1,f(T,\omega^{1-i}))}$, where $f$ is the associated Iwasawa power series. It is expected that $CG_m^i$ and $IACG^i_m$ be isomorphic, providing us ...

- Contributors
- Elledge, Shawn Michael, Childress, Nancy, Bremner, Andrew, et al.
- Created Date
- 2013

Extremal graph theory results often provide minimum degree conditions which guarantee a copy of one graph exists within another. A perfect $F$-tiling of a graph $G$ is a collection $\mathcal{F}$ of subgraphs of $G$ such that every element of $\mathcal{F}$ is isomorphic to $F$ and such that every vertex in $G$ is in exactly one element of $\mathcal{F}$. Let $C^{3}_{t}$ denote the loose cycle on $t = 2s$ vertices, the $3$-uniform hypergraph obtained by replacing the edges $e = \{u, v\}$ of a graph cycle $C$ on $s$ vertices with edge triples $\{u, x_e, v\}$, where $x_e$ is uniquely assigned ...

- Contributors
- Oursler, Roy, Czygrinow, Andrzej, Kierstead, Hal A, et al.
- Created Date
- 2019

The uncrossing partially ordered set $P_n$ is defined on the set of matchings on $2n$ points on a circle represented with wires. The order relation is $\tau'\leq \tau$ in $P_n$ if and only if $\tau'$ is obtained by resolving a crossing of $\tau$. %This partial order has been studied by Alman-Lian-Tran, Huang-Wen-Xie, Kenyon, and Lam. %The posets $P_n$ emerged from studies of circular planar electrical networks. Circular planar electrical networks are finite weighted undirected graphs embedded into a disk, with boundary vertices and interior vertices. By Curtis-Ingerman-Morrow and de Verdi\`ere-Gitler-Vertigan, the electrical networks can be encoded with response matrices. By ...

- Contributors
- Kim, Younghwan, Fishel, Susanna, Bremner, Andrew, et al.
- Created Date
- 2018

A tiling is a collection of vertex disjoint subgraphs called tiles. If the tiles are all isomorphic to a graph $H$ then the tiling is an $H$-tiling. If a graph $G$ has an $H$-tiling which covers all of the vertices of $G$ then the $H$-tiling is a perfect $H$-tiling or an $H$-factor. A goal of this study is to extend theorems on sufficient minimum degree conditions for perfect tilings in graphs to directed graphs. Corrádi and Hajnal proved that every graph $G$ on $3k$ vertices with minimum degree $delta(G)ge2k$ has a $K_3$-factor, where $K_s$ is the complete graph on $s$ ...

- Contributors
- Molla, Theodore, Kierstead, Henry A, Czygrinow, Andrzej, et al.
- Created Date
- 2013