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Title

Distribution of integer partitions with large number of summands

Authors 1

Affiliations

  1. Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan

Bibliography

  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.
  3. N. G. de Bruijn, On Mahler's partition problem, Indag. Math. 10 (1948), 210-220.
  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.
  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.
  6. P. Flajolet, X. Gourdon and P. Dumas, Mellin transforms and asymptotics: harmonic sums, Theoret. Comput. Sci. 144 (1995), 3-58.
  7. B. Fristedt, The structure of random partitions of large integers, Trans. Amer. Math. Soc. 337 (1993), 703-735.
  8. C. B. Haselgrove and H. N. V. Temperley, Asymptotic formulae in the theory of partitions, Proc. Cambridge Philos. Soc. 50 (1954), 225-241.
  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.
  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.
  16. W. B. Pennington, On Mahler's partition problem, Ann. of Math. 57 (1953), 531-546.
  17. L. B. Richmond, The moments of partitions, I, Acta Arith. 26 (1975), 411-425.
  18. L. B. Richmond, Mahler's partition problem, Ars Combin. 2 (1976), 169-189.
  19. L. B. Richmond, The moments of partitions, II, Acta Arith. 28 (1975), 229-243.
  20. L. B. Richmond, Some general problems on the number of parts in partitions, Acta Arith. 66 (1994), 297-313.
  21. W. Schwarz, Einige Anwendungen Tauberscher Sätze in der Zahlentheorie. C. Mahler's Partitionsproblem, J. Reine Angew. Math. 228 (1967), 182-188
  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.
  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.
  24. G. Szekeres, Some asymptotic formulae in the theory of partitions II, Quart. J. Math. Oxford 4 (1953), 96-111.
  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.
Acta Arithmetica
1996-1997/78/4
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Pages:
351-365
Main language of publication
English
Received
1996-03-27
Accepted
1996-08-16
Published
1997
Exact and natural sciences