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References
- V. Baladi and B. Vallée, Euclidean algorithms are Gaussian, J. Number Theory 110 (2005), 331-386. Math. Review 2006e:11192
- D. W. Boyd and H. L. Montgomery, Cyclotomic partitions, in Number Theory (Banff, AB, 1988), 7-25, de Gruyter, Berlin, 1990. Math. Review 92b:11073
- H.-H. Chern and H.-K. Hwang, Phase changes in random m-ary search trees and generalized quicksort. Random Structures Algorithms 19 (2001), 316-358. Math. Review 2002k:68040
- H. Delange, Généralisation du théorème de Ikehara, Ann. Sci. Éc. Norm. Supér. 71 (1954), 213-242. Math. Review 16,921e
- H. Delange, Sur les moments des fonctions additives, Acta Arith. 49 (1988), 213-236. Math. Review 89h:11048
- M. Deléglise, M. O. Hernane and J.-L. Nicolas, Grandes valeurs et nombres champions de la fonction arithmétique de Kalmár, J. Number Theory 128 (2008), 1676-1716. Math. Review 2009d:11137
- P. Erdös, On some asymptotic formulas in the theory of the ``factorisatio numerorum," Ann. of Math 42 (1941) 989-993; Corrections, ibid. 44 (1943) 647-651. Math. Review 3,165b
- P. Flajolet and A. Odlyzko, Singularity analysis of generating functions, SIAM J. Discrete Math. 3 (1990), 216-240. Math. Review 90m:05012
- P. Flajolet and M. Soria, General combinatorial schemas: Gaussian limit distributions and exponential tails. Discrete Math. 114 (1993), 159-180. Math. Review 94e:05021
- P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, Cambridge, UK, 2009.
- P. Flajolet and B. Vallée, Continued fraction algorithms, functional operators, and structure constants, Theoret. Comput. Sci. 194 (1998), 1-34. Math. Review 98j:11061
- P. Flajolet and I. Vardi, Zeta function expansions of classical constants, unpublished manuscript; available at http://algo.inria.fr/flajolet/Publications/landau.ps
- E. Hille, A problem in ``factorisatio numerorum," Acta Arith. 2 (1936), 134-144.
- H.-K. Hwang, Théorèmes limites pour les structures combinatories et les fonctions arithmétiques, Ph. D. Thesis, École Polytechnique, 1994.
- H.-K. Hwang, Distribution of the number of factors in random ordered factorizations of integers, J. Number Theory 81 (2000), 61-92. Math. Review 2001k:11183
- L. Kalmár, A ``factorisatio numerorum" problémájáról, Mat. Fiz. Lapok 38 (1931) 1-15.
- A. Knopfmacher, J. Knopfmacher and R. Warlimont, Ordered factorizations for integers and arithmetical semigroups, in Advances in Number Theory (Kingston, ON, 1991), 151-165, Oxford Univ. Press, New York, 1993. Math. Review 97e:11118
- A. Knopfmacher and M. E. Mays, A survey of factorization counting functions, Int. J. Number Theory 1 (2005), 563-581. Math. Review 2006j:11047
- J. Korevaar, Tauberian Theory. A Century of Developments, Springer-Verlag, Berlin, 2004. Math. Review 2006e:11139
- Y.-K. Lau, Local distribution of ordered factorizations of integers, J. Number Theory 91 (2001), 312-317. Math. Review 2003e:11103
- P. A. MacMahon, The theory of perfect partitions and the compositions of multipartite numbers, Mess. Math. 20 (1891), 103-119.
- W. Narkiewicz, Number Theory, Translated from the Polish by S. Kanemitsu. World Scientific Publishing Co., Singapore; distributed by Heyden & Son, Inc., Philadelphia, PA, 1983. Math. Review 85j:11002
- L. A. Newberg and D. Naor, A lower bound on the number of solutions to the probed partial digest problem. Adv. in Appl. Math. 14 (1993), 172-183. Math. Review 1218242
- G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Second edition, Société Mathématique de France, Paris, 1995; English translation published by Cambridge University Press, 1995. Math. Review 97e:11005a
- B. Vallée, Dynamical analysis of a class of Euclidean algorithms, Theoret. Comput. Sci. 297 (2003), 447-486. Math. Review 2004e:11144
- H. S. Wilf, The Redheffer matrix of a partially ordered set, Electron. J. Combin. 11 (2004/06), Research Paper 10, 5 pp. Math. Review 2005i:050070L>

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