On coincidences of tuples in a q-ary tree with random labels of vertices
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Vasiliy I. Kruglov
Abstract
Let all vertices of a complete q-ary tree of finite height be independently and equiprobably labeled by the elements of some finite alphabet. We consider the numbers of pairs of identical tuples of labels on chains of subsequent vertices in the tree. Exact formulae for the expectations of these numbers are obtained, convergence to the compound Poisson distribution is proved. For the size of cluster composed by pairs of identically labeled chains we also obtain exact formula for the expectation.
Originally published in Diskretnaya Matematika (2018) 30,№3, 48–67 (in Russian).
Funding
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.
Acknowledgement
The author expresses his deep gratitude to his research supervisor A.M.~Zubkov for initial problem statement and numerous discussions throughout the study.
References
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A subcritical decomposable branching process in a mixed environment
- Limit theorems for bounded branching processes
- On coincidences of tuples in a q-ary tree with random labels of vertices
- A generalization of Shannon function
- Reduced critical Bellman–Harris branching processes for small populations
- Estimates of the mean size of the subset image under composition of random mappings
- Necessary conditions for power commuting in finite-dimensional algebras over a field
Articles in the same Issue
- Frontmatter
- A subcritical decomposable branching process in a mixed environment
- Limit theorems for bounded branching processes
- On coincidences of tuples in a q-ary tree with random labels of vertices
- A generalization of Shannon function
- Reduced critical Bellman–Harris branching processes for small populations
- Estimates of the mean size of the subset image under composition of random mappings
- Necessary conditions for power commuting in finite-dimensional algebras over a field
