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arXiv · 0710.0447

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

Florent Hivert·Jean-Christophe Novelli·Lenny Tevlin·Jean-Yves Thibon
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Abstract

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.

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Florent Hivert, Jean-Christophe Novelli, Lenny Tevlin, Jean-Yves Thibon. 2007-10-02. Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers. https://arxiv.org/abs/0710.0447

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