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A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK

Bellissimo, Michael Robert
http://rave.ohiolink.edu/etdc/view?acc_num=akron1523039734121649

Abstract Details

2018, Master of Science, University of Akron, Mathematics.
Our goal is to be able to determine the distance between two partitions in the same Rouquier block. This paper explores a lower bound on the number of steps required to get from the quotient of a partition lambda; to (empty set, empty set, ..., (w)). We will use the Young diagrams in the quotient of lambda and a process of right and left steps to obtain a new partition that is connected to lambda in the Brauer graph of these representations. Paired with this process we will incorporate a notation called the badness of each box in the Young diagram representation of the quotient of lambda;. This will allow us to show that the lower bound on the number of steps is less than or equal to the initial badness, b, of the starting partition divided by the maximum reduction of badness by each right and left step, 2w^2.
James P. Cossey, Dr. (Advisor)
Jeffery M. Riedl, Dr. (Committee Member)
Stefan Forcey, Dr. (Committee Member)
Kevin L. Kreider, Dr. (Committee Chair)
55 p.
Mathematics
partitions; badness; Rouquier Block; representation theory; combinatorics; Brauer Graph; diameter of a Brauer Graph; partition theory; Young Diagram; decomposition matrix; p-core; abacus; p-regular partitions; Littlewood-Richardson Rule

Recommended Citations

Citations

  • Bellissimo, M. R. (2018). A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1523039734121649

    APA Style (7th edition)

  • Bellissimo, Michael. A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK. 2018. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1523039734121649.

    MLA Style (8th edition)

  • Bellissimo, Michael. "A LOWER BOUND ON THE DISTANCE BETWEEN TWO PARTITIONS IN A ROUQUIER BLOCK." Master's thesis, University of Akron, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1523039734121649

    Chicago Manual of Style (17th edition)

akron1523039734121649
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This open access ETD is published by University of Akron and OhioLINK.