#### Date of Graduation

Spring 2016

#### Document Type

Honors Research Project

#### Degree Name

Bachelor of Science

#### Major

Mathematics

#### Research Sponsor

James Cossey

#### First Reader

Jeffrey Riedl

#### Second Reader

Stefan Forcey

#### Abstract

For my Honors Research Project, I will be researching special properties of Rouquier blocks that represent the partitions of integers. This problem is motivated by ongoing work in representation theory of the symmetric group. For each integer n and each prime p, there is an object called a Rouquier block; this block can be visualized as a collection of points in a plane, each corresponding to a partition. In this group of points, we say a pair of points is “connected” if certain conditions on the partitions are met. We compare each partition with each other partition, add edges when we can, and we end up with a collection of points that are connected by some number of edges (note that two points are not connected by a line if the conditions are not met).

In my project, I will be finding a formula that will restrict the diameter of this graph. I want to minimize the distance between the two points that are the furthest away from each other. A formula to give the most efficient path is either impossible to find or is too complicated to be useful; rather, I will set a ceiling on this distance, so that, given any two blocks, I can give the largest “most efficient” path length possible.

#### Recommended Citation

Mayer, Andrew, "The Diameter of a Rouquier Block" (2016). *Honors Research Projects*. 333.

https://ideaexchange.uakron.edu/honors_research_projects/333

#### Included in

Algebra Commons, Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons

## Comments

Additional research is in progress and new developments discussed in the conclusion may come forth in the future.