Decomposable combinatorial structures are studied with restricted patterns. We focus on the decomposable structures in the exp-log class. Using the method of analysis of singularities introduced by Flajolet and Odlyzko [5], we provide an estimate for the probability that a decomposable structure of size n has a given restricted pattern. We exemplify with several decomposable structures like permutations and polynomials over finite fields.

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Keywords Decomposable structures, Exp-log class, Generating functions, Labeled and unlabeled structures, Restricted pattern
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Journal Annals of Combinatorics
Dong, L. (Li), Gao, Z, & Panario, D. (2009). Enumeration of decomposable combinatorial structures with restricted patterns. Annals of Combinatorics, 12(4), 357–372. doi:10.1007/s00026-009-0008-y