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  • On the Remaining Cases of the Kang Park Conjecture in Partition Theory

    Creator:
    Sturman, Leah
    Abstract:
    In 1956, Alder conjectured an integer partition inequality which generalized Euler’s partition identity, the first Rogers-Ramanujan identity, and a partition identity of Schur. Alder’s conjecture, proved in part by Andrews in 1971, followed by Yee in 2008, and finally completed by Alfes, Jameson, and Lemke Oliver in 2010 states that...
    Resource Type:
    Dissertation
    Full Text:
    Remaining Cases of the Kang Park Conjecture in Partition Theory Abstract approved: Holly Swisher In 1956

  • Zeros of Replicable Functions

    Creator:
    Toomey, Benjamin J.
    Abstract:
    Following the work of Asai, Kaneko, and Ninomiya for Faber polynomials associated to the modular group, and Bannai, Kojima, and Miezaki's partial proof for the case of the Fricke group of level 2, we show that the zeros of certain modular functions for some low-level genus zero groups associated to...
    Resource Type:
    Dissertation
    Full Text:
    : Zeros of Replicable Functions Abstract approved: Holly M. Swisher Following the work of Asai, Kaneko

  • Existence of Eta-Quotients for Squarefree Levels and Modular Type Supercongruences for Hypergeometric Functions

    Creator:
    Allen, Michael
    Abstract:
    In this dissertation, we consider two problems in number theory, both relating to modular forms. First we consider when a given modular form can be expressed as a quotient in Dedekind's $\eta$ function. Rouse and Webb \cite{RW} have determined the integers $N \leq 500$ such that the graded ring of...
    Resource Type:
    Dissertation
    Full Text:
    Functions Abstract approved: Holly Swisher In this dissertation, we consider two problems in number

  • Establishing Several Infinite Families of Mock and Quantum Modular Forms

    Creator:
    Arnold-Roksandich, Allison F.
    Abstract:
    In 2013, Lemke Oliver created a list of all eta-quotients which are theta functions. Then in 2016, Folsom, Garthwaite, Kang, Swisher, and Treneer utilized this list of ``eta-theta'' functions along with Zwegers's construction of mock theta functions to create a set of mock modular forms which are also quantum modular...
    Resource Type:
    Dissertation
    Full Text:
    approved: Holly M. Swisher In 2013, Lemke Oliver created a list of all eta-quotients which are theta

  • De Bruijn graphs and their applications to fault tolerant networks

    Creator:
    Baker, Joel
    Abstract:
    The goal of this expository paper is to introduce De Bruijn graphs and discuss their applications to fault tolerant networks.
    Resource Type:
    Capstone Project

  • Zeros of Certain Combinations of Products of Eisenstein Series

    Creator:
    Klangwang, Jetjaroen
    Abstract:
    In this dissertation, we begin by presenting the result of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of the Eisenstein series for the full modular group in the standard fundamental domain. Their simple but beautiful argument shows that all zeros are located on the lower...
    Resource Type:
    Dissertation
    Full Text:
    Certain Combinations of Products of Eisenstein Series Abstract approved: Holly M. Swisher In this

  • Overpartition Ranks, Cranks, and Frobenius Representations

    Creator:
    Morrill, Thomas
    Abstract:
    We generalize overpartition rank and crank generating functions to obtain k-fold variants, and give a combinatorial interpretation for each. The k-fold crank generating function is interpreted by extending the first and second residual cranks to a natural infinite family. The k-fold rank generating functions generate two families of buffered Frobenius...
    Resource Type:
    Dissertation
    Full Text:
    , Cranks, and Frobenius Representations Abstract approved: Holly M. Swisher We generalize overpartition

  • Periodicity and Partition Congruences

    Creator:
    Al-Saedi, Ali Hammood
    Abstract:
    In this note, we generalize recent work of Mizuhara, Sellers, and Swisher that gives a method for establishing restricted plane partition congruences based on a bounded number of calculations. Using periodicity for partition functions, our extended technique could be a useful tool to prove congruences for certain types of combinatorial...
    Resource Type:
    Dissertation
    Full Text:
    Partition Congruences Abstract approved: Holly M. Swisher In this note, we generalize recent work of

  • The Collision of Quadratic Fields, Binary Quadratic Forms, and Modular Forms

    Creator:
    Smith, Karen
    Abstract:
    As indicated by the title The Collision of Quadratic Fields, Binary Quadratic Forms, and Modular Forms, this paper leads us to an understanding of the relationship between these three areas of study. In [4], Zagier gives the results of an intriguing example of the relationship between these areas. However there...
    Resource Type:
    Capstone Project

  • The j-Function and the Monster

    Creator:
    Scherer, Asa
    Abstract:
    The first published notion that the j-function was in any way related to the Monster came in 1979, when Conway and Norton noted in [CN79] that each coefficient in the q- expansion of the j-function could be written as a (nontrivial) integral linear combination of the dimensions of irreducible representations...
    Resource Type:
    Capstone Project