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

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

Bibliographic Details
Main Author: Trinh, Megan
Language:English
Published: University of Akron / OhioLINK 2018
Subjects:
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
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=akron152304291682246
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-akron1523042916822462021-08-03T07:05:53Z On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group Trinh, Megan 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 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. 2018-06-08 English text University of Akron / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=akron152304291682246 http://rave.ohiolink.edu/etdc/view?acc_num=akron152304291682246 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic 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
spellingShingle 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
Trinh, Megan
On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group
author Trinh, Megan
author_facet Trinh, Megan
author_sort Trinh, Megan
title On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group
title_short On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group
title_full On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group
title_fullStr On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group
title_full_unstemmed On the Diameter of the Brauer Graph of a Rouquier Block of the Symmetric Group
title_sort on the diameter of the brauer graph of a rouquier block of the symmetric group
publisher University of Akron / OhioLINK
publishDate 2018
url http://rave.ohiolink.edu/etdc/view?acc_num=akron152304291682246
work_keys_str_mv AT trinhmegan onthediameterofthebrauergraphofarouquierblockofthesymmetricgroup
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