Browsing Mathematics by Author "Billey, Sara"
Now showing items 19 of 9

A Complete Implementation of Graphlopedia: A Fingerprint Database for Graphs
Chandra, SharatThe OEIS is a widely used and incredibly powerful tool to catalogue usersubmitted 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 ThomasSince ReinerStantonWhite 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 (20140224)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 WalkerRecent 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, AustinIn 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 PatrickThis 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 ... 
LamWilliams Markov chains on symmetric groups
Huynh, Anh Trung (20140224)This paper reviews the current state of the LamWilliams 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 (20131114)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 TimothyWe 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 ...