Quelques exemples de suites unimodales en théorie des nombres
Journal de Théorie des Nombres de Bordeaux, Volume 2 (1990) no. 1, pp. 13-30.
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Michel Balazard. Quelques exemples de suites unimodales en théorie des nombres. Journal de Théorie des Nombres de Bordeaux, Volume 2 (1990) no. 1, pp. 13-30. doi : 10.5802/jtnb.17. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.17/

1 G. Almkvist, Proof of a conjecture about unimodal polynomials, J. of Number Theory 32 (1989), 43-57. | MR: 1002113 | Zbl: 0678.05002

2 G.E. Andrews, The theory of partitions, Addison-Wesley (1976), Reading. | MR: 557013 | Zbl: 0371.10001

3 M. Balazard, H. Delange et J.-L. Nicolas, Sur le nombre de facteurs premiers des entiers, C.R.A.S. 306 série I (1988), 511-514. | MR: 941613 | Zbl: 0644.10032

4 M. Balazard, Comportement statistique du nombre de facteurs premiers des entiers, Séminaire de Th. des Nombres, Paris 1987-1988, (1990), 1-21, Birkhaüser. | MR: 1042762 | Zbl: 0689.10047

5 M. Balazard, Unimodalité de la distribution du nombre des diviseurs premiers d'un entier. A paraître aux Annales de l'Institut Fourier. | EuDML: 74877 | Numdam | Zbl: 0711.11030

6 L. Comtet, Analyse combinatoire (1970), P.U.F, Paris.

7 S. Dharmadikari et K. Joag-Dev, Unimodality, convexity and applications (1988), Academic Press, New-York. | MR: 954608 | Zbl: 0646.62008

8 P. Erdös, On the integers having exactly k prime factors, Annals of Math. 49 (1948), 53-66. | MR: 23279 | Zbl: 0030.29604

9 P. Erdös et G. Tenenbaum, Sur les densités de certaines suites d'entiers, Proc. London Math. Soc. (3)59 (1989), 417-438. | MR: 1014865 | Zbl: 0694.10040

10 H. Gerber et J. Keilson, Some results for discrete unimodality, J. Amer. Statist. Assoc. 66 (1971), 386-389. | Zbl: 0236.60017

11 D. Hensley, The distribution of round numbers, Proc. London Math. Soc. (3) 54 (1987), 412-444. | MR: 879393 | Zbl: 0588.10047

12 A. Hildebrand et G. Tenenbaum, On the number of prime factors of an integer, Duke Math. J. 56 (1988), 471-501. | MR: 948530 | Zbl: 0655.10036

13 J.W. Hughes, Lie algebraic proofs of some theorems on partitions, Number Theory and Algebra (H. Zassenhaus, ed.) (1977), Academic Press, New-York. | MR: 491213 | Zbl: 0372.10010

14 J.-L. Nicolas, Sur la distribution des entiers ayant une quantité fixée de facteurs premiers, Acta Arith. 44 (1984), 191-200. | MR: 774099 | Zbl: 0512.10034

15 A.M. Odlyzko et L.B. Richmond, On the compositions of an integer, Combinatorial Mathematics VII. Proceedings (1979), 199-210, (R.W. Robinson et al. ed.). Springer Lecture Notes 829. | MR: 611195 | Zbl: 0451.05009

16 A.M. Odlyzko et L.B. Richmond, On the unimodality of some partition polynomials, Europ. J. Combinatorics 2 (1982), 69-84. | MR: 656013 | Zbl: 0482.10015

17 A.M. Odlyzko et L.B. Richmond, On the unimodality of high powers of discrete distributions, Annals of Probability 13 (1985), 299-306. | MR: 770644 | Zbl: 0561.60021

18 C. Pomerance, On the distribution of round numbers, Number Theory (K. Alladi ed.), (Proc. Ootacamund, India, 1984), 173-200, Springer Lecture Notes 1122. | MR: 797790 | Zbl: 0565.10038

19 K.F. Roth et G. Szekeres, Some asymptotic formulae in the theory of partitions, Quart. J. Math. Oxford (2) 5 (1954), 241-259. | MR: 67913 | Zbl: 0057.03902

20 A. Selberg, Note on a paper by L.G. Sathe, J. Indian Math. Soc. 18 (1954), 83-87. | MR: 67143 | Zbl: 0057.28502

21 R.P. Stanley, Unimodal sequences arising from Lie algebras, Alfred Young Day Proceedings (T.V. Narayona, R.M. Mathsen and J.G. Williams eds.) (1980), Marcel Dekker, New-York. | MR: 588199 | Zbl: 0451.05004

22 R.P. Stanley, Log-concave and unimodal sequences in algebra, combinatories and geometry, Prépublication.

23 G. Szekeres, Some asymptotic formulae in the theory of partitions (II), Quart. J. Math. Oxford (2) 4 (1953), 96-111. | MR: 57279 | Zbl: 0050.04101

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