Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Asymptotic relations for partitions


Author: L. B. Richmond
Journal: Trans. Amer. Math. Soc. 219 (1976), 379-385
MSC: Primary 10J20
DOI: https://doi.org/10.1090/S0002-9947-1976-0412137-2
MathSciNet review: 0412137
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Asymptotic relations are obtained for the number $ {p_A}(n)$ of partitions of the integer n into summands from a set A of integers. The set A is subject to certain conditions; however the only arithmetic condition is that A have property $ {P_k}$ of Bateman and Erdös. A conjecture of Bateman and Erdös concerning the kth differences of $ {p_A}(n)$ may be verified using these asymptotic relations.


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

  • [1] P. T. Bateman and P. Erdös, Monotonicity of partition functions, Mathematica 3 (1956), 1-14. MR 18, 195. MR 0080121 (18:195a)
  • [2] L. B. Richmond, Asymptotic relations for partitions, J. Number Theory 7 (1975), 389-405. MR 0382210 (52:3095)
  • [3] -, The moments of partitions. II, Acta Arith. (to appear). MR 0401687 (53:5514)
  • [4] K. F. Roth and G. Szekeres, Some asymptotic formulae in the theory of partitions, Quart. J. Math. Oxford Ser. (2) 5 (1954), 244-259. MR 16, 797. MR 0067913 (16:797b)
  • [5] L. B. Richmond, Asymptotic results for partitions. II; Conjecture of Bateman and Erdös, J. Number Theory (to appear).

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 10J20

Retrieve articles in all journals with MSC: 10J20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0412137-2
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society