On Foulkes characters

  title={On Foulkes characters},
  author={Alexander R. Miller},
  journal={Mathematische Annalen},
  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. 

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