Finite differences of the partition function
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- by Hansraj Gupta PDF
- Math. Comp. 32 (1978), 1241-1243 Request permission
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 ${n_0}(r)/{r^3}\sim 1$.References
- Hansraj Gupta, Two theorems in partitions, Indian J. Math. 14 (1972), 7–8. MR 327653 H. GUPTA, C. E. GWYTHER & J. C. P. MILLER, Tables of Partitions, University Press, Cambridge, 1958.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 1241-1243
- MSC: Primary 10A45
- DOI: https://doi.org/10.1090/S0025-5718-1978-0480319-5
- MathSciNet review: 0480319