Given integers m and n, we study the probability that structures of size n have all components of size at most m. The results are given in term of a generalized Dickman function of n/m.

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Keywords Decomposable combinatorial structures, Dickman function, Largest components, Permutations, Polynomials over finite fields
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Journal Algorithmica
Omar, M. (Mohamed), Panario, D, Richmond, B. (Bruce), & Whitely, J. (Jacki). (2006). Asymptotics of largest components in combinatorial structures. In Algorithmica (Vol. 46, pp. 493–503). doi:10.1007/s00453-006-0103-y