Some asymptotic results on finite vector spaces
Advances in Applied Mathematics
Gaussian limiting distributions for the number of components in combinatorial structures
Journal of Combinatorial Theory Series A
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Journal of Computational and Applied Mathematics - Special issue on asymptotic methods in analysis and combinatorics
General combinatorial schemas: Gaussian limit distributions and exponential tails
Discrete Mathematics - Special issue on combinatorics and algorithms
Marking in combinatorial constructions: generating functions and limiting distributions
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
Asymptotic expansions for the Stirling numbers of the first kind
Journal of Combinatorial Theory Series A
Combinatorial Enumeration
Journal of Computational and Applied Mathematics
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Given a class of combinatorial structures 𝒞, we consider the quantity N(n, m), the number of multiset constructions 𝒫 (of 𝒞) of size n having exactly m 𝒞-components. Under general analytic conditions on the generating function of 𝒞, we derive precise asymptotic estimates for N(n, m), as n→∞ and m varies through all possible values (in general 1≤m≤n). In particular, we show that the number of 𝒞-components in a random (assuming a uniform probability measure) 𝒫-structure of size n obeys asymptotically a convolution law of the Poisson and the geometric distributions. Applications of the results include random mapping patterns, polynomials in finite fields, parameters in additive arithmetical semigroups, etc. This work develops the ‘additive’ counterpart of our previous work on the distribution of the number of prime factors of an integer [20].