## 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.

- Jones, John
- 9 Arizona State University
- 8 Fishel, Susanna
- 7 Childress, Nancy
- 5 Bremner, Andrew
- 4 Czygrinow, Andrzej
- 3 Spielberg, John
- more
- 2 Colbourn, Charles
- 1 AL-SULEIMAN, SULTAN
- 1 Barcelo, Helene
- 1 Carrillo, Benjamin
- 1 Elledge, Shawn Michael
- 1 Franks, Chase Leroyce
- 1 Kaliszewski, Steven
- 1 Kierstead, Hal A
- 1 Kierstead, Henry
- 1 Nelson, Luke Edwin
- 1 Nguyen, Tho Xuan
- 1 Oursler, Roy
- 1 Paupert, Julien
- 1 Quigg, John
- 1 Spielberg, Jack
- 1 Treat, Kevin
- 1 Zinzer, Scott

- 9 English

- 9 Public

- Mathematics
- 2 Maximal Chains
- 2 Tamari Lattices
- 1 $\lambda$-invariant
- 1 Cambrian Lattices
- 1 Catalan lattice
- 1 Degree
- more
- 1 Diophantine equations
- 1 Enumeration
- 1 Gamma-transform
- 1 Graph
- 1 Higher Stasheff-Tamari order
- 1 Hypergraph
- 1 Iwasawa Invariant
- 1 Iwasawa Theory
- 1 Iwasawa theory
- 1 Iwasawa theory 11R23
- 1 Lambda modules
- 1 Lattices
- 1 Limits
- 1 Loose Cycle
- 1 Pseudo-polynomial
- 1 Rainbow Cycle
- 1 Tamari lattice
- 1 Theoretical mathematics
- 1 Tiling
- 1 algebraic number theory
- 1 elliptic curve
- 1 elliptic curve Chabauty
- 1 elliptic curves
- 1 m-eralized Cambrian Lattices
- 1 number theory
- 1 p-adic Valued Measure
- 1 p-adic analysis
- 1 profinite groups 20E18

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- 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

In Iwasawa theory, one studies how an arithmetic or geometric object grows as its field of definition varies over certain sequences of number fields. For example, let $F/\mathbb{Q}$ be a finite extension of fields, and let $E:y^2 = x^3 + Ax + B$ with $A,B \in F$ be an elliptic curve. If $F = F_0 \subseteq F_1 \subseteq F_2 \subseteq \cdots F_\infty = \bigcup_{i=0}^\infty F_i$, one may be interested in properties like the ranks and torsion subgroups of the increasing family of curves $E(F_0) \subseteq E(F_1) \subseteq \cdots \subseteq E(F_\infty)$. The main technique for studying this sequence of curves when ...

- Contributors
- Franks, Chase Leroyce, Childress, Nancy, Barcelo, Helene, et al.
- Created Date
- 2011

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

In 1984, Sinnott used $p$-adic measures on $\mathbb{Z}_p$ to give a new proof of the Ferrero-Washington Theorem for abelian number fields by realizing $p$-adic $L$-functions as (essentially) the $Gamma$-transform of certain $p$-adic rational function measures. Shortly afterward, Gillard and Schneps independently adapted Sinnott's techniques to the case of $p$-adic $L$-functions associated to elliptic curves with complex multiplication (CM) by realizing these $p$-adic $L$-functions as $Gamma$-transforms of certain $p$-adic rational function measures. The results in the CM case give the vanishing of the Iwasawa $mu$-invariant for certain $mathbb{Z}_p$-extensions of imaginary quadratic fields constructed from torsion points of CM elliptic curves. In ...

- Contributors
- Zinzer, Scott, Childress, Nancy, Bremner, Andrew, et al.
- Created Date
- 2015

Diophantine arithmetic is one of the oldest branches of mathematics, the search for integer or rational solutions of algebraic equations. Pythagorean triangles are an early instance. Diophantus of Alexandria wrote the first related treatise in the fourth century; it was an area extensively studied by the great mathematicians of the seventeenth century, including Euler and Fermat. The modern approach is to treat the equations as defining geometric objects, curves, surfaces, etc. The theory of elliptic curves (or curves of genus 1, which are much used in modern cryptography) was developed extensively in the twentieth century, and has had great application ...

- Contributors
- Nguyen, Tho Xuan, Bremner, Andrew, Childress, Nancy, et al.
- Created Date
- 2019

The Cambrian lattice corresponding to a Coxeter element c of An, denoted Camb(c), is the subposet of An induced by the c-sortable elements, and the m-eralized Cambrian lattice corresponding to c, denoted Cambm(c), is dened as a subposet of the braid group accompanied with the right weak ordering induced by the c-sortable elements under certain conditions. Both of these families generalize the well-studied Tamari lattice Tn rst introduced by D. Tamari in 1962. S. Fishel and L. Nelson enumerated the chains of maximum length of Tamari lattices. In this dissertation, I study the chains of maximum length of the Cambrian ...

- Contributors
- AL-SULEIMAN, SULTAN, Fishel, Susanna, Childress, Nancy, et al.
- Created Date
- 2017

The Tamari lattices have been intensely studied since they first appeared in Dov Tamari’s thesis around 1952. He defined the n-th Tamari lattice T(n) on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Despite their interesting aspects and the attention they have received, a formula for the number of maximal chains in the Tamari lattices is still unknown. The purpose of this thesis is to convey my results on progress toward the solution of this problem and to discuss future work. A few years ago, Bergeron and Préville-Ratelle generalized ...

- Contributors
- Nelson, Luke Edwin, Fishel, Susanna, Czygrinow, Andrzej, et al.
- Created Date
- 2016