Characters of symmetric groups: sharp bounds and applications

@article{Larsen2008CharactersOS,
  title={Characters of symmetric groups: sharp bounds and applications},
  author={Michael Larsen and Aner Shalev},
  journal={Inventiones mathematicae},
  year={2008},
  volume={174},
  pages={645-687}
}
We provide new estimates on character values of symmetric groups which hold for all characters and which are in some sense best possible. It follows from our general bound that if a permutation σ∈Sn has at most no(1) cycles of length <m, then |χ(σ)|≤χ(1)1/m+o(1) for all irreducible characters χ of Sn. This is a far reaching generalization of a result of Fomin and Lulov.We then use our various character bounds to solve a wide range of open problems regarding mixing times of random walks… Expand
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