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Unital versions of the higher order peak algebras

Abstract : We construct unital extensions of the higher order peak algebras defined by Krob and the third author in [Ann. Comb. 9 (2005), 411―430], and show that they can be obtained as homomorphic images of certain subalgebras of the Mantaci-Reutenauer algebras of type $B$. This generalizes a result of Bergeron, Nyman and the first author [Trans. AMS 356 (2004), 2781―2824].
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Marcelo Aguiar, Jean-Christophe Novelli, Jean-Yves Thibon. Unital versions of the higher order peak algebras. 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009), 2009, Hagenberg, Austria. pp.13-24, ⟨10.46298/dmtcs.2729⟩. ⟨hal-00823077⟩



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