Generalized descent patterns in permutations and associated Hopf algebras

J.-C. Novelli , C. Reutenauer , J.-Y. Thibon

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keywords algebrasconsecutivefunctionshopfletterspatternspermutationsassociated

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Descents in permutations or words are defined from the relative position of two consecutive letters. We investigate a statistic involving patterns of k consecutive letters, and show that it leads to Hopf algebras generalizing noncommutative symmetric functions and quasi-symmetric functions.

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Generalized descent patterns in permutations and associated Hopf algebras

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