On Exponential Growth of Degrees

@article{Roichman2015OnEG,
  title={On Exponential Growth of Degrees},
  author={Yuval Roichman},
  journal={Electron. J. Comb.},
  year={2015},
  volume={22},
  pages={2}
}
A short proof to a recent theorem of Giambruno and Mishchenko is given in this note. 1 The theorem The following theorem was recently proved by Giambruno and Mishchenko. Theorem 1. [1, Theorem 1] For every 0 1 and n0 ∈ N, such that for every partition λ of n > n0 with max{λ1, λ1} β. The proof of Giambruno and Mishchenko is rather complicated and applies a clever order on the cells of the Young diagram. It should be noted that Theorem 1 is an immediate consequence of Rasala’s lower bounds on… 

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Degrees of irreducible characters of the symmetric group and exponential growth

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