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1996-1997 | 78 | 4 | 351-365
Tytuł artykułu

Distribution of integer partitions with large number of summands

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
78
Numer
4
Strony
351-365
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-03-27
poprawiono
1996-08-16
Twórcy
  • Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav78i4p351bwm
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