On Foulkes characters

@article{Miller2021OnFC,
  title={On Foulkes characters},
  author={Alexander R. Miller},
  journal={Mathematische Annalen},
  year={2021},
  volume={381},
  pages={1589 - 1614}
}
Orthogonality relations for Foulkes characters of full monomial groups are presented, along with three solutions to the problem of decomposing products of these characters, and new applications, including a product reformulation of a Markov chain for adding random numbers studied by Diaconis and Fulman, and a new proof of a theorem of Zagier which generalizes one of Harer and Zagier on the enumeration of Riemann surfaces of a given genus. 

The characters of symmetric groups that depend only on length

. The characters χ ( π ) of S n that depend only on the number of cycles of π are completely determined.

Numerator polynomials of Riordan matrices

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The author recently introduced Foulkes characters for a wide variety of reflection groups, and the hyperoctahedral ones have attracted some special attention. Diaconis and Fulman connected them to