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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Finite differences of the partition function


Author: Hansraj Gupta
Journal: Math. Comp. 32 (1978), 1241-1243
MSC: Primary 10A45
MathSciNet review: 0480319
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Abstract: From the Hardy-Ramanujan-Rademacher formula for $ p(n)$--the number of unrestricted partitions of n, it is not difficult to deduce that there exists a least positive integer $ {n_0}(r)$ such that $ {V^r}p(n) \geqslant 0$ for each $ n \geqslant {n_0}(r)$, where $ Vp(n) = p(n) - p(n - 1)$ and $ {V^r}p(n) = V\{ {V^{r - 1}}p(n)\} $. In this note, we give values of $ {n_0}(r)$ for each $ r \leqslant 10$ and conjecture that $ {n_0}(r)/{r^3}\sim1$.


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

  • [1] Hansraj Gupta, Two theorems in partitions, Indian J. Math. 14 (1972), 7–8. MR 0327653 (48 #5995)
  • [2] H. GUPTA, C. E. GWYTHER & J. C. P. MILLER, Tables of Partitions, University Press, Cambridge, 1958.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1978-0480319-5
PII: S 0025-5718(1978)0480319-5
Article copyright: © Copyright 1978 American Mathematical Society