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)

 

Divisibility properties of the $ q$-tangent numbers


Authors: George E. Andrews and Ira Gessel
Journal: Proc. Amer. Math. Soc. 68 (1978), 380-384
MSC: Primary 05A15
MathSciNet review: 0462960
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The q-tangent number $ {T_{2n + 1}}(q)$ is shown to be divisible by $ (1 + q)(1 + {q^2}) \cdots (1 + {q^n})$. Related divisibility questions are discussed.


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

  • [1] George E. Andrews, The theory of partitions, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. Encyclopedia of Mathematics and its Applications, Vol. 2. MR 0557013 (58 #27738)
  • [2] Louis Comtet, Advanced combinatorics, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974. The art of finite and infinite expansions. MR 0460128 (57 #124)
  • [3] I. Gessel, Exponential generating functions $ \pmod p$ and their q-analogs (in prep.).
  • [4] Richard P. Stanley, Binomial posets, Möbius inversion, and permutation enumeration, J. Combinatorial Theory Ser. A 20 (1976), no. 3, 336–356. MR 0409206 (53 #12968)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05A15

Retrieve articles in all journals with MSC: 05A15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0462960-0
PII: S 0002-9939(1978)0462960-0
Article copyright: © Copyright 1978 American Mathematical Society