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Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers |
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| Authors: | Florent Hivert Jean-Christophe Novelli Lenny Tevlin Jean-Yves Thibon |
| Institution: | (1) LITIS, Université de Rouen, Avenue de l’université, 76801 Saint étienne du Rouvray, France;(2) Institut Gaspard Monge, Université Paris-Est Marne-la-Vallée, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France;(3) Physics Department, Yeshiva University, 500 West 185th Street, New York, NY 10033, USA |
| 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. |
| Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 05E05 15A15 16W30 |
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