Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Divisibility by $ 2$ of Stirling-like numbers


Author: Donald M. Davis
Journal: Proc. Amer. Math. Soc. 110 (1990), 597-600
MSC: Primary 11B73
MathSciNet review: 1036984
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a characterization of functions of the form $ f(n) = \nu (n - E)$, where $ \nu ( - )$ denotes the exponent of 2, and $ E$ is a $ 2$-adic integer. We show that it applies to the restriction to even or odd integers of the function $ f(n) = \nu (a{5^n} + b{3^n} + c)$, with mild restrictions on $ a,b$, and $ c$. This function is closely related to divisibility of certain Stirling numbers of the second kind.


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

  • [1] F. Clarke, Hensel's lemma and the divisibility by primes of Stirling numbers of the second kind (to appear).
  • [2] Louis Comtet, Advanced combinatorics, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974. The art of finite and infinite expansions. MR 0460128
  • [3] M. C. Crabb and K. Knapp, The Hurewicz map on stunted complex projective spaces, Amer. J. Math. 110 (1988), no. 5, 783–809. MR 961495, 10.2307/2374693
  • [4] Albert T. Lundell, Generalized 𝐸-invariants and the numbers of James, Quart. J. Math. Oxford Ser. (2) 25 (1974), 427–440. MR 0375312
  • [5] Albert T. Lundell, A divisibility property for Stirling numbers, J. Number Theory 10 (1978), no. 1, 35–54. MR 0460135

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 11B73

Retrieve articles in all journals with MSC: 11B73


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1036984-4
Keywords: Stirling numbers, divisibility by 2, $ 2$-adic integers
Article copyright: © Copyright 1990 American Mathematical Society