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MR2052597 20C30 (05A05 05E15 20F55)
Aguiar, Marcelo; Bergeron, Nantel; Nyman, Kathryn The peak algebra and the descent algebras of types $B$ and $D$. Trans. Amer. Math. Soc. 356 (2004), no. 7, 2781–2824.
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