Browsing Mathematics by Author "Billey, Sara"

Now showing items 1-9 of 9

    • A Complete Implementation of Graphlopedia: A Fingerprint Database for Graphs 

      Chandra, Sharat
      The OEIS is a widely used and incredibly powerful tool to catalogue user-submitted sequences of interest to the mathematical community, and to associate with them a list of citations where these sequences can be found. In ...

    • Applications of the Cyclic Sieving Phenomenon to Words, Branching Rules, and Tableaux 

      Ahlbach, Connor Thomas
      Since Reiner-Stanton-White defined the cyclic sieving phenomenon associated to a finite cyclic group action and a polynomial, many compelling examples of cyclic sieving have been found. In this thesis, we focus on what we ...

    • Combinatorial Laguerre Series 

      Taylor, Jair Patrick (2014-02-24)
      We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials. We describe how such a series can be computed by ...

    • Cycle type factorizations in the finite general linear groups 

      Gordon, Graham Walker
      Recent work by Huang, Lewis, Morales, Reiner, and Stanton suggests that the regular elliptic elements of $\mathrm{GL}_n \mathbb{F}_q$ are somehow analogous to the $n$-cycles of the symmetric group. In 1981, Stanley enumerated ...

    • Dual Equivalence Graphs and their Applications 

      Roberts, Austin
      In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph whose vertices are weighted by Ira Gessel's ...

    • Formal group laws and hypergraph colorings 

      Taylor, Jair Patrick
      This thesis demonstrates a connection between formal group laws and chromatic symmetric functions of hypergraphs, two seemingly unrelated topics in the theory of symmetric functions. A formal group law is a symmetric ...

    • Lam-Williams Markov chains on symmetric groups 

      Huynh, Anh Trung (2014-02-24)
      This paper reviews the current state of the Lam-Williams conjectures on a multivariate Markov chain on the symmetric group S_n. We start with Lam's work on random core partitions which led to a remarkable Markov chain on ...

    • Mathematical Aspects of Gerrymandering 

      Solbrig, Mary Katherine (2013-11-14)
      Every 10 years the United States performs a census, and this census determines how many members of congress will represent each state. Then begins an unfortunate battle, as cartographers manipulate the boundaries for ...

    • The Sandpile Group on a Hexagonal Grid 

      Johnson, Eli Timothy
      We introduce the notion of an abelian sandpile, including the basic definitions, its use as a model, and some of the foundational theorems and observations. We describe a constructive method for reducing redundant ...