Article contents
Part Sizes of Smooth Supercritical Compositional Structures
Published online by Cambridge University Press: 09 July 2014
Abstract
We define the notion of smooth supercritical compositional structures. Two well-known examples are compositions and graphs of given genus. The ‘parts’ of a graph are the subgraphs that are maximal trees. We show that large part sizes have asymptotically geometric distributions. This leads to asymptotically independent Poisson variables for numbers of various large parts. In many cases this leads to asymptotic formulas for the probability of being gap-free and for the expected values of the largest part sizes, number of distinct parts and number of parts of multiplicity k.
- Type
- Paper
- Information
- Combinatorics, Probability and Computing , Volume 23 , Issue 5: Honouring the Memory of Philippe Flajolet - Part 1 , September 2014 , pp. 686 - 716
- Copyright
- Copyright © Cambridge University Press 2014
References
- 2
- Cited by