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Bounding the Maximal Character Degree in terms of Smaller Degrees in the Symmetric Groups

Soomro, Sadaf Komal

Abstract Details

2018, Master of Science, University of Akron, Mathematics.
The symmetric group of degree n, denoted as S_n, is defined to be the group of permutations on a set with cardinality n, thereby consisting of n! total permutations. In this paper, we bound the maximal irreducible character degree of S_n in terms of smaller degrees of the irreducible characters. Specifically, we demonstrate that for every integer n ≥ 106, ∑{χ ∈ Irr(S_n)} {χ(1) < b(S_n)} χ(1)² > 4b(S_n)² where Irr(S_n) represents the set of irreducible complex characters of S_n, b(S_n) represents the largest degree of a character of Irr(S_n), and χ(1) represents the degree of a character of Irr(S_n).
Hung Nguyen (Advisor)
Jeffrey Riedl (Committee Member)
James Cossey (Committee Member)
38 p.

Recommended Citations

Citations

  • Soomro, S. K. (2018). Bounding the Maximal Character Degree in terms of Smaller Degrees in the Symmetric Groups [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1525706168900092

    APA Style (7th edition)

  • Soomro, Sadaf. Bounding the Maximal Character Degree in terms of Smaller Degrees in the Symmetric Groups . 2018. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1525706168900092.

    MLA Style (8th edition)

  • Soomro, Sadaf. "Bounding the Maximal Character Degree in terms of Smaller Degrees in the Symmetric Groups ." Master's thesis, University of Akron, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1525706168900092

    Chicago Manual of Style (17th edition)