Abstract
Let đn be a semigroup of mappings of the n-element set X into itself and đn(A) be a subset of mappings from đn such that sizes of all their components belong to the set A. By Ïn = Ïn(A) we denote a random mapping having uniform distribution on the set đn(A). Such mappings were considered by A. N. Timashev in 2019. For some class of sets A having positive densities in the set N of natural numbers the asymptotic of cardinalities of sets đn(A) is found for n â â. Also the estimate for the total variation distance between the structure of the mapping Ïn(A) and corresponding sequence of independent Poisson random variables is obtained.
Originally published in Diskretnaya Matematika (2023) 35, â3, 143â163 (in Russian).
Funding statement: The research was supported by the Russian Science Foundation under grant no.19-11-00111-P, https://rscf.ru/en/project/19-11-00111/, and performed at Steklov Mathematical Institute of Russian Academy of Sciences.
Acknowledgment
The author is grateful to the reviewer for valuable comments, which made it possible to avoid a number of inaccuracies in the manuscript and improve the presentation.
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Artikel in diesem Heft
- Frontmatter
- Generation of n-quasigroups by proper families of functions
- Boolean functions constructed using digital sequences of linear recurrences
- On the sets of the propagation criterion for strict majority Boolean functions
- Branching processes in random environment with freezing
- Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Binary Matrix Rank Test»
- On random mappings with restrictions on sizes of components
Artikel in diesem Heft
- Frontmatter
- Generation of n-quasigroups by proper families of functions
- Boolean functions constructed using digital sequences of linear recurrences
- On the sets of the propagation criterion for strict majority Boolean functions
- Branching processes in random environment with freezing
- Limit joint distribution of the statistics of «Monobit test», «Frequency Test within a Block» and «Binary Matrix Rank Test»
- On random mappings with restrictions on sizes of components