Largest component in random combinatorial structures

Discrete Mathematics

Volumn 180, Issue 1-3, 1998, Pages 185-209

  Gourdon, Xavier ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042357388     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(97)00115-5     Document Type: Article

References (22)

1. J. Arney, E.D. Bender, Random mappings with constraints on coalescence and number of origins, Pacific J. Math. 103 (1982) 269-294.
2. N.G. DeBruijn, On the number of positive integers ≤ x and free of prime factors > y, Indag. Math. 13 (1951) 2-121.
3. N.G. DeBruijn, On the number of positive integers ≤x and free of prime factors > y, Indag. Math. 28 (1966) 239-247.
4. K. Dickman, On the frequency of numbers containing prime factors of a certain relative magnitude. Ark. Mat. Astr. Fys. 22 (1930) 1-14.
5. W. Feller, An Introduction to Probability Theory and Its Applications, vol. 2. Wiley, New York, 1971.
6. P. Flajolel, X. Gourdon, P. Dumas, Mellin transforms and asymptotics: harmonic sums. Theoret. Comput. Sci. (Special Volume on Mathematical Analysis of Algorithms) 144 (1-2) June (1985) 3-58.
7. P. Flajolet, A.M. Odlyzko, Random mapping statistics, in: J.-J. Quisquater, J. Vandewalle (eds.) Advances in Cryptology, Proc. Eurocrypt'89 Houtalen, Belgium, April 1989. pp. 329-354, Lecture Notes in Computer Science, vol. 434, Springer, Berlin, 1990.
8. P. Flajolet, A.M. Odlyzko, Singularity analysis of generating functions, SIAM J. Discrete Math. 3(2) (1990) 216-240.
9. P. Flajolet, B. Salvy, P. Zimmermann, Automatic average-case analysis of algorithms. Theoret. Comput. Sci. Ser. A. 79 (1) (1991) 37-109.
10. P. Flajolet, M. Soria, The cycle construction. SIAM J. Discrete Math. 4(1) (1991) 58-60.
11. P. Flajolet, M. Sonia, General combinatorial schemas: gaussian limit distributions and exponential tails. Discrete Math. 114(1993) 159-180.
12. X. Gourdon, H. Prodinger. Random subgraphs of the n-cycle. Discrete Math., accepted, short communication. 1995.
13. A. Joyal. Une Théorie combinatoire des séries formelles. Adv. Math. 42(1) (1981) 1-82.
14. D.E. Knuth, The average time for carry propagation. Indag. Math. 40 (1978) 238-242.
15. A. Meir, J.W. Moon. On the altitude of modes in random trees, Canad. J. Math. 30 (1978) 997-1015.
16. A. Meir, J.W. Moon. On random mapping patterns. Combinatorica 4 (1984) 61-70.
17. R. Otter, The number of trees, Ann. Math. 49(3) (1948) 583-599.
18. J.-J. Quisquater. J.-P. Delescaille, How easy is collision search'? Application to DES, in: Proc. of EUROCRYPT'89, Lecture Notes in Computer Science, vol. 434, Springer. Berlin, 1989, pp. 429-433.
19. P. Révész, Strong theorems in coin tossing, in: Proc. 1978 Internat. Congr. Mathematicians. Helsinki, 1980.
20. L.A. Shepp, S.P. Lloyd, Ordered cycle lengths in a random permutation, Trans. Amer. Math. Soc. 121 (1966) 340-357.
21. M. Soria-Cousineau, Méthodes d'analyse pour les constructions combinatoires et les algorithmes. Doctorat d'état. Université de Paris-Sud, Orsay. July 1990.
22. V.E. Stepanov, Limit distributions of certain characteristics of random mappings, Theory Probab. Appl. 14 (1969) 612-626.