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Diameter of a Rouquier block

Mayer, Andrew
http://rave.ohiolink.edu/etdc/view?acc_num=akron1523279464229599

Abstract Details

2018, Master of Science, University of Akron, Mathematics.
This paper will be researching special properties of Rouquier blocks of partitions of integers. This problem is motivated by ongoing work in representation theory of the symmetric group. For each choice of integer parameters w and p with p = 2 and w = 1, 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. In this paper, we will be finding a formula that will restrict the diameter of this graph. We 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, we will set a ceiling on this distance, so that, given any two blocks, we will know the largest “most efficient” path length possible. Once this is done, we will also extend our problem to find the largest degree in a graph.
James Cossey, Dr. (Advisor)
Jeffrey Riedl, Dr. (Committee Member)
Stefan Forcey, Dr. (Committee Member)
Kevin Kreider, Dr. (Committee Chair)
Mathematics; Theoretical Mathematics
Rouquier; block; blocks; diameter; graph; degree; Littlewood-Richardson; Littlewood; Richardson; weight; abacus; Young; diagram; representation; partition

Recommended Citations

Citations

  • Mayer, A. (2018). Diameter of a Rouquier block [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1523279464229599

    APA Style (7th edition)

  • Mayer, Andrew. Diameter of a Rouquier block. 2018. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1523279464229599.

    MLA Style (8th edition)

  • Mayer, Andrew. "Diameter of a Rouquier block." Master's thesis, University of Akron, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1523279464229599

    Chicago Manual of Style (17th edition)

akron1523279464229599
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This open access ETD is published by University of Akron and OhioLINK.