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Article Dans Une Revue Selecta Mathematica Année : 2009

Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers

Résumé

We prove conjectures of the third author [L. Tevlin, Proc. FPSAC'07, Tianjin] on two new bases of noncommutative symmetric functions: the transition matrices from the ribbon basis have nonnegative integral coefficients. This is done by means of two composition-valued statistics on permutations and packed words, which generalize the combinatorics of Genocchi numbers.

Dates et versions

hal-00484691 , version 1 (18-05-2010)

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Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon. Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers. Selecta Mathematica, 2009, 15 (1), pp.105-119. ⟨10.1007/s00029-009-0489-x⟩. ⟨hal-00484691⟩
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