Foulkes characters, Eulerian idempotents, and an amazing matrix

@article{Diaconis2011FoulkesCE,
  title={Foulkes characters, Eulerian idempotents, and an amazing matrix},
  author={P. Diaconis and Jason Fulman},
  journal={Journal of Algebraic Combinatorics},
  year={2011},
  volume={36},
  pages={425-440}
}
John Holte (Am. Math. Mon. 104:138–149, 1997) introduced a family of “amazing matrices” which give the transition probabilities of “carries” when adding a list of numbers. It was subsequently shown that these same matrices arise in the combinatorics of the Veronese embedding of commutative algebra (Brenti and Welker, Adv. Appl. Math. 42:545–556, 2009; Diaconis and Fulman, Am. Math. Mon. 116:788–803, 2009; Adv. Appl. Math. 43:176–196, 2009) and in the analysis of riffle shuffling (Diaconis and… Expand
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