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On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group

Trinh, Megan
http://rave.ohiolink.edu/etdc/view?acc_num=akron152304291682246

Abstract Details

2018, Master of Science, University of Akron, Mathematics.
In this paper, we examine a certain graph related to the representation theory of the symmetric group. This graph is called the Brauer graph of a Rouquier block. It is known that the diameter d(R) of this graph satisfies the following condition: the diameter d(R) is between p - 1 and two times the ceiling function of "log base two of w" + p + 2 where p and w are certain associated parameters. Note that the preceding condition describes both a lower bound and an upper bound on the diameter d(R). We conjecture that the best upper bound for the diameter is actually between p - 1 and the ceiling function of "log base 2 of w" + p. We conjecture that two vertices in our graph have the maximum distance between them, and we prove that this distance is at most the ceiling function of "log base 2 of w" + p by exhibiting an algorithm that creates a path between these two vertices.
James Cossey, Ph.D. (Advisor)
Jeffrey Riedl, Ph.D. (Committee Member)
Stefan Forcey, Ph.D. (Committee Member)
Kevin Kreider, Ph.D. (Committee Chair)
48 p.
Mathematics
mathematics; partitions; combinatorics; Rouquier block; abacus; Young diagram; weight; quotient; Littlewood-Richardson Rule; Chuang-Tan Rule; Brauer graphs; hook length; rim hook; representation theory

Recommended Citations

Citations

  • Trinh, M. (2018). On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron152304291682246

    APA Style (7th edition)

  • Trinh, Megan. On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group. 2018. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron152304291682246.

    MLA Style (8th edition)

  • Trinh, Megan. "On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group." Master's thesis, University of Akron, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron152304291682246

    Chicago Manual of Style (17th edition)

akron152304291682246
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This open access ETD is published by University of Akron and OhioLINK.