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Degrees of irreducible characters of the symmetric group and exponential growth

Authors: Antonio Giambruno and Sergey Mishchenko
Journal: Proc. Amer. Math. Soc. 144 (2016), 943-953
MSC (2010): Primary 20C30, 05A17
Published electronically: October 6, 2015
MathSciNet review: 3447648
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Abstract: We consider sequences of degrees of ordinary irreducible $ S_n$-
characters. We assume that the corresponding Young diagrams have rows and columns bounded by some linear function of $ n$ with leading coefficient less than one. We show that any such sequence has at least exponential growth and we compute an explicit bound.

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Antonio Giambruno
Affiliation: Dipartimento di Matematica e Informatica, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy

Sergey Mishchenko
Affiliation: Department of Algebra and Geometric Computations, Ulyanovsk State University, Ulyanovsk 432017, Russia

Keywords: Symmetric group, character, exponential growth
Received by editor(s): June 6, 2014
Received by editor(s) in revised form: February 5, 2015
Published electronically: October 6, 2015
Communicated by: Patricia Hersh
Article copyright: © Copyright 2015 American Mathematical Society

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