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Limit theorems for sizes of trees in the unlabelled graph of a random mapping
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Yu. L. Pavlov
Published/Copyright:
August 1, 2004
We find limit distributions of the maximum size of a tree and of the number of trees of given size in an unlabelled random forest consisting of N rooted trees and n non-root vertices provided that N, n → ∞ so that 0 < C1 ≤ N / √n ≤ C2 < ∞. With the use of these results, for the unlabelled graph of a random single-valued mapping of the set {1, 2, . . .,n} into itself we prove theorems on the limit behaviour of the maximum tree size and of the number of trees of size r as n → ∞ in the cases of fixed r and r/n1/3 ≥ C3 > 0.
Published Online: 2004-08-01
Published in Print: 2004-08-01
Copyright 2004, Walter de Gruyter
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Articles in the same Issue
- Limit theorems for sizes of trees in the unlabelled graph of a random mapping
- The limit distribution of the number of cyclic vertices in a random mapping in a special case
- The joint distribution of the number of ones and the number of 1-runs in binary Markov sequences
- Polynomial transformations of GEO-rings of prime characteristic
- On optimal exact coverings of a graph in the class of weakly dense bases
- On a generalisation of the method of boundary functionals
- On characteristic polynomials of periodic graphs
