Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The $ q$-tangent and $ q$-secant numbers via basic Eulerian polynomials


Authors: Dominique Foata and Guo-Niu Han
Journal: Proc. Amer. Math. Soc. 138 (2010), 385-393
MSC (2000): Primary 05A15, 05A30, 05E15
Published electronically: October 2, 2009
MathSciNet review: 2557155
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The classical identity that relates Eulerian polynomials to tangent numbers together with the parallel result dealing with secant numbers is given a $ q$-extension, both analytically and combinatorially. The analytic proof is based on a recent result by Shareshian and Wachs and the combinatorial one on the geometry of alternating permutations.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 05A15, 05A30, 05E15

Retrieve articles in all journals with MSC (2000): 05A15, 05A30, 05E15


Additional Information

Dominique Foata
Affiliation: Institut Lothaire, 1 rue Murner, F-67000 Strasbourg, France
Email: foata@math.u-strasbg.fr

Guo-Niu Han
Affiliation: Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René-Descartes, F-67084 Strasbourg, France
Email: guoniu@math.u-strasbg.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10144-2
PII: S 0002-9939(09)10144-2
Keywords: $q$-tangent numbers, $q$-secant numbers, $q$-Eulerian polynomials, excedances, derangements, desarrangements, alternating permutations.
Received by editor(s): October 6, 2008
Published electronically: October 2, 2009
Communicated by: Jim Haglund
Article copyright: © Copyright 2009 American Mathematical Society