Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T09:01:47.934Z Has data issue: false hasContentIssue false
  • English
  • Français

Partitions into distinct large parts

Published online by Cambridge University Press:  09 April 2009

Gregory A. Freiman  and
Jane Pitman
Gregory A. Freiman
Affiliation:
School of Mathematical Sciences, Raymond and Beverly Sacler Faculty of Exact Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel
Jane Pitman
Affiliation:
Department of Pure Mathematics, University of Adelaide, S.A. 5005, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An asymptotic estimate is obtained for the number of partitions of the positive integer n into distinct parts, each of which is at least m. The estimate holds uniformly with respect to positive m such that m = o(n(log n)−9), as n → ∞.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 3 , December 1994 , pp. 386 - 416
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Breiman, L., Probability (Addison-Wesley, Reading, 1968).Google Scholar
[2]Dixmier, J. and Nicolas, J.-L., ‘Partitions sans petits sommants’, in: A Tribute to Paul Erdös (eds. Baker, A., Bollobás, B. and Hajmal, A.) (Cambridge University Press, Cambridge, 1990) pp. 121–152.CrossRefGoogle Scholar
[3]Erdös, P., Nicolas, J.-L. and Szalay, M., ‘Partitions into parts which are unequal and large’, preprint, Inst. Hautes Études Sci. Publ. Math., 1990.CrossRefGoogle Scholar
[4]Erdös, P. and Szalay, M., ‘On the statistical theory of partitions’, in: Topics in classical number theory, Coll. Math. Soc. Janos Bolyai 34 (North-Holland/Elsevier, Budapest, 1981) pp. 397–450.Google Scholar
[5]Freiman, G., ‘Waring's problem with an increasing number of terms’, Elabuz. Gos. Ped. Inst. Učen. Zap. 3 (1958), 105–119 (in Russian).Google Scholar
[6]Freiman, G., ‘An analytical method of analysis of linear Boolean equations’, in: Third Int. Conf. on Collective Phenomena (Moscow, 1978),Google Scholar
Ann. New York Acad. Sci. 337 (New York Acad. Sci., New York, 1980) pp. 97–102.Google Scholar
[7]Freiman, G., ‘On extremal additive problems of Paul Erdös’, in: Proc. of Second Int. Conf. on Combinatorial Mathematics and Computing, Canberra, 1987, Ars Combin. 26B (1988) pp. 93–114.Google Scholar
[8]Hardy, G. H. and Ramanujan, S., ‘Asymptotic formulae in combinatory analysis’, Proc. London Math. Soc. (2) 17 (1918), 75–115CrossRefGoogle Scholar
(Also in Collected Papers of S. Ramanujan, (Cambridge Univ. Press, Cambridge, 1927), (Chelsea, New York, 1962) pp. 276–309).Google Scholar
[9]Hua, L. K., ‘On the number of partitions of a number into unequal parts’, Trans. Amer. Math. Soc. 51 (1942), 194–201.CrossRefGoogle Scholar
[10]Postnikov, A. G., Vvedenie v analitičeskuiu teoriu ˇisel (in Russian), translated as Introduction to analytic number theory, Translations of Mathematical Monographs 68 (Amer. Math. Soc., Providence, 1987).Google Scholar
[11]Roth, K. and Szekeres, G., ‘Some asymptotic formulae in the theory of partitions’, Quart. J. Math. Oxford Ser. (2) 5 (1954), 241–259.CrossRefGoogle Scholar