Distribution of integer partitions with large number of summands
Acta Arithmetica (1997)
- Volume: 78, Issue: 4, page 351-365
- ISSN: 0065-1036
Access Full Article
topHow to cite
topHsien-Kuei Hwang. "Distribution of integer partitions with large number of summands." Acta Arithmetica 78.4 (1997): 351-365. <http://eudml.org/doc/206955>.
@article{Hsien1997,
author = {Hsien-Kuei Hwang},
journal = {Acta Arithmetica},
keywords = {Mellin transforms; saddle-point method; asymptotic behavior; number of integer partitions; large number of summands; sieve of Eratosthenes; partitions into parts; limit distribution; number of summands in random partitions},
language = {eng},
number = {4},
pages = {351-365},
title = {Distribution of integer partitions with large number of summands},
url = {http://eudml.org/doc/206955},
volume = {78},
year = {1997},
}
TY - JOUR
AU - Hsien-Kuei Hwang
TI - Distribution of integer partitions with large number of summands
JO - Acta Arithmetica
PY - 1997
VL - 78
IS - 4
SP - 351
EP - 365
LA - eng
KW - Mellin transforms; saddle-point method; asymptotic behavior; number of integer partitions; large number of summands; sieve of Eratosthenes; partitions into parts; limit distribution; number of summands in random partitions
UR - http://eudml.org/doc/206955
ER -
References
top- [1] G. E. Andrews, The Theory of Partitions, Encyclopedia Math. Appl. 2, Addison-Wesley, 1976.
- [2] F. C. Auluck, S. Chowla and H. Gupta, On the maximum value of the number of partitions of n into k parts, J. Indian Math. Soc. 6 (1942), 105-112. Zbl0063.00139
- [3] N. G. de Bruijn, On Mahler's partition problem, Indag. Math. 10 (1948), 210-220. Zbl0030.34502
- [4] J. Dixmier et J.-L. Nicolas, Partitions sans petits sommants, in: A Tribute to Paul Erdős, A. Baker, B. Bollobás and A. Hajnal (eds.), Cambridge University Press, 1990, 120-152. Zbl0719.11067
- [5] P. Erdős and J. Lehner, The distribution of the number of summands in the partitions of a positive integer, Duke Math. J. 8 (1941), 335-345. Zbl0025.10703
- [6] P. Flajolet, X. Gourdon and P. Dumas, Mellin transforms and asymptotics: harmonic sums, Theoret. Comput. Sci. 144 (1995), 3-58. Zbl0869.68057
- [7] B. Fristedt, The structure of random partitions of large integers, Trans. Amer. Math. Soc. 337 (1993), 703-735. Zbl0795.05009
- [8] C. B. Haselgrove and H. N. V. Temperley, Asymptotic formulae in the theory of partitions, Proc. Cambridge Philos. Soc. 50 (1954), 225-241. Zbl0055.27401
- [9] H.-K. Hwang, Limit theorems for the number of summands in integer partitions, submitted.
- [10] H.-K. Hwang, Sur la répartition des valeurs des fonctions arithmétiques, I. Le nombre de facteurs premiers d'un entier, submitted.
- [11] H.-K. Hwang and Y.-N. Yeh, Distribution of integer partitions with a small number of summands, in preparation.
- [12] D. V. Lee, The asymptotic distribution of the number of summands in unrestricted Λ-partitions, Acta Arith. 65 (1993), 29-43.
- [13] G. Meinardus, Asymptotische Aussagen über Partitionen, Math. Z. 59 (1954), 388-398. Zbl0055.03806
- [14] W. Narkiewicz, Number Theory, World Scientific, Singapore, 1983 (translated by S. Kanemitsu).
- [15] J.-L. Nicolas, Sur la distribution des nombres ayant une quantité fixée de facteurs premiers, Acta Arith. 44 (1984), 191-200. Zbl0512.10034
- [16] W. B. Pennington, On Mahler's partition problem, Ann. of Math. 57 (1953), 531-546. Zbl0050.04005
- [17] L. B. Richmond, The moments of partitions, I, Acta Arith. 26 (1975), 411-425. Zbl0314.10036
- [18] L. B. Richmond, Mahler's partition problem, Ars Combin. 2 (1976), 169-189. Zbl0347.10039
- [19] L. B. Richmond, The moments of partitions, II, Acta Arith. 28 (1975), 229-243. Zbl0318.10034
- [20] L. B. Richmond, Some general problems on the number of parts in partitions, Acta Arith. 66 (1994), 297-313. Zbl0823.11059
- [21] W. Schwarz, Einige Anwendungen Tauberscher Sätze in der Zahlentheorie. C. Mahler's Partitionsproblem, J. Reine Angew. Math. 228 (1967), 182-188 Zbl0156.27704
- [22] M. Szalay and P. Turán, On some problems of the statistical theory of partitions with application to characters of the symmetric group I, Acta Math. Acad. Sci. Hungar. 29 (1977), 361-379. Zbl0371.10033
- [23] M. Szalay and P. Turán, On some problems of the statistical theory of partitions with application to characters of the symmetric group II, Acta Math. Acad. Sci. Hungar., 381-392. Zbl0371.10034
- [24] G. Szekeres, Some asymptotic formulae in the theory of partitions II, Quart. J. Math. Oxford 4 (1953), 96-111. Zbl0050.04101
- [25] G. Szekeres, Asymptotic distribution of partitions by number and size of parts, in: Number Theory, Colloq. Math. Soc. János Bolyai 51, North-Holland, 1987, 527-538.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.