Measures of Distinctness for Random Partitions and Compositions of an Integer

Advances in Applied Mathematics

Volumn 19, Issue 3, 1997, Pages 378-414

  Hwang, H K ^a   Yeh, Y N ^a  

^a INSTITUTE OF MATHEMATICS   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001187704     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1006/aama.1997.0555     Document Type: Article

References (55)

1. Actor A. A. Infinite products, partition functions, and the Meinardus theorem. J. Math. Phys. 35:1994;5749-5764.
2. Almkvist G. Exact asymptotic formulas for the coefficients of nonmodular functions. J. Number Theory. 38:1991;145-160.
3. Andrews G. E. The theory of partitions. Encyclopedia of Mathematics and Its Applications. 1976;Addison-Wesley, Reading.
4. G. E. Andrews, 1986, q, CBMS Regional Conference Series in Mathematics, 66, American Mathematical Society, Providence, RI.
5. Arató M., Benczúr A. Dynamic placement of records and the classical occupancy problem. Comput. Math. Appl. 7:1981;173-185.
6. k(n. J. Indian Math. Soc. 6:1942;113-114.
7. Ayoub R. An introduction to the analytic theory of numbers. Mathematical Surveys. 10:1963;American Mathematical Society, Providence.
8. Baxter R. J. Exactly Solved Models in Statistical Mechanics. 1982;Academic Press, London.
9. Chen W.-C. Limit theorems for general size distributions. J. Appl. Probab. 18:1981;139-147.
10. Cipra B. A. An introduction to the Ising model. Amer. Math. Monthly. 94:1987;937-959.
11. Diaconis P., Graham R. L. Spearman's footrule as a measure of disarray. J. Roy. Soc. Statist. Ser. B. 39:1977;262-268.
12. Diaconis P., Holmes S., Janson S., Lalley S., Pemantle R. Metrics on compositions and coincidences among renewal sequences. Aldous D., Pemantle R. Random Discrete Structures. IMA Volumes in Mathematics and its Applications. 76:1996;81-101 Springer, New York.
13. Erdélyi A. Higher Transcendental Functions. 1953;Krieger Publishing, Malabar.
14. Erdos P., Lehner J. The distribution of the number of summands in the partitions of a positive integer. Duke Math. J. 8:1941;335-345.
15. Erdos P., Szalay M. On the statistical theory of partitions. Colloq. Math. Soc. János Bolyai. 34:1981;397-450.
16. Flajolet P., Gardy D., Thimonier L. Birthday paradox, coupon collectors, caching algorithms and self-organizing search. Discrete Appl. Math. 39:1992;207-229.
17. Flajolet P., Gourdon X., Dumas P. Mellin transforms and asymptotics: harmonic sums. Theoret. Comput. Sci. 144:1995;3-58.
18. P. Flajolet, X. Gourdon, D. Panario, 1996, Random polynomial factorization.
19. Flajolet P., Odlyzko A. M. Singularity analysis of generating functions. SIAM J. Discrete Math. 3:1990;216-240.
20. Flajolet P., Soria M. The cycle construction. SIAM J. Discrete Math. 4:1991;58-60.
21. Goh W. M. Y., Schmutz E. The number of distinct part sizes in random integer partitions. J. Combin. Theory Ser. A. 69:1995;149-158.
22. Goodman L. A., Kruskal W. H. Measures of Association for Cross Classifications. Springer Series in Statistics. 1:1979;Springer-Verlag, New York.
23. X. Gourdon, H. Prodinger, A generating function approach to random subgraphs of then, Discrete Math.
24. Guibas L. J., Odlyzko A. M. Long repetitive patterns in random sequences. Z. Wahrsch. Verw. Gebiete. 53:1980;241-262.
25. Hardy G. H. An Introduction to the Theory of Numbers. 1978;Oxford Science Publications, Oxford.
26. H.-K. Hwang, Limit theorems for the number of summands in integer partitions.
27. Hwang H.-K. Théorèmes Limites pour les Structures Combinatorics et les Fonctions Arithmétiques. 1994;Ecole Polytechnique.
28. Johnson N. L., Kotz S. Urn Models and their Applications. An Approach to Modern Discrete Probability Theory. 1977;Wiley, New York.
29. Kendall M., Gibbons J. D. Rank Correlation Methods. 1990;Arnold, London.
30. Kingman J. F. C. Random partitions in population genetics. Proc. Roy. Soc. London Ser. A. 361:1978;1-20.
31. A. Knopfmacher, M. E. Mays, Compositions withm, Ars Combinatorica.
32. A. Knopfmacher, M. E. Mays, The sum of distinct parts in compositions and partitions.
33. Knuth D. E. The average time for carry propagation. Indag. Math. 40:1978;238-242.
34. Knuth D. E. The Art of Computer Programming. 1981;Addison-Wesley, Reading.
35. Kolchin V. F., Sevast'yanov R. A., Chistyakov V. P. Random Allocations. 1978;Winston, Washington.
36. Larralde H., Weiss G. H. A generating function for the second moment of the distinct number of sites visited by ann. J. Phys. A. 28:1995;5217-5225.
37. Mannila H. Measures of presortedness and optimal sorting algorithms. IEEE Trans. Comput. 34:1985;318-325.
38. Meinardus G. Asymptotische Aussagen über Partitionen. Math. Z. 59:1954;388-398.
39. Odlyzko A. M., Richmond B. On the compositions of an integer. Lecture Notes in Mathematics. 829:1979;Springer, Berlin. p. 199-209.
40. Ramanujan S. Hardy G. H., Seshu P. V. Collected Papers of Srinivasa Ramanujan. 1962;Chelsea, New York.
41. Richmond L. B. Asymptotic relations for partitions. Trans. Amer. Math. Soc. 219:1976;379-385.
42. Richmond L. B. The moments of partitions, II. Acta Arith. 28:1976;229-243.
43. Richmond L. B. Some general problems on the number of parts in partitions. Acta Arith. 64:1994;297-313.
44. Richmond L. B., Knopfmacher A. Compositions with distinct parts. Aequationes Math. 49:1995;86-97.
45. Schmutz E. Part sizes of random integer partitions. Indian J. Pure Appl. Math. 25:1994;567-575.
46. Shparlinski I. E. Computational and Algorithmic Problems in Finite Fields. 1992;Kluwer Academic, Dordrecht.
47. Szalay M., Turán P. On some problems of the statistical theory of partitions with application to characters of the symmetric group, I. Acta Math. Hungar. 29:1977;361-379.
48. Szekeres G. An asymptotic formula in the theory of partitions. Quart. J. Math. Oxford Ser. 2:1951;85-108.
49. Temperley H. N. V. Statistical mechanics and the partition of numbers I. The transition of liquid helium. Proc. Roy. Soc. Ser. A. 199:1949;361-375.
50. Vitter J. S., Chen W.-C. Design and Analysis of Coaslesced Hashing. 1987;Oxford University Press, Oxford.
51. Warlimont R. Factorisatio numerorum with constraints. J. Number Theory. 45:1993;186-199.
52. Whittaker E. T., Watson G. N. A Course of Modern Analysis. 1927;Cambridge University Press, Cambridge.
53. Wigert S. Sur la série de Lambert et ses application à la théorie des nombres. Acta Math. 41:1918;197-218.
54. Wilcoxon F. Individual comparisons by ranking methods. Biometrics. 1:1945;80-83.
55. Wilf H. Three problems in combinatorial asymptotics. J. Combin. Theory Ser. A. 35:1983;199-207.