Logarithmic Combinatorial Structures: A Probabilistic Approach

@inproceedings{Arratia2003LogarithmicCS,
  title={Logarithmic Combinatorial Structures: A Probabilistic Approach},
  author={Richard Arratia and Andrew D. Barbour and Simon Tavar{\'e}},
  year={2003}
}
The elements of many classical combinatorial structures can be naturally decomposed into components. Permutations can be decomposed into cycles, polynomials over a finite field into irreducible factors, mappings into connected components. In all of these examples, and in many more, there are strong similarities between the numbers of components of different sizes that are found in the decompositions of `typical' elements of large size. For instance, the total number of components grows… 

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