Moment Characteristics of a Random Mapping with Restrictions on Component Sizes
Let be the semigroup of mappings of an -element set into itself. For a set , denote by the family of those mappings in whose component sizes belong to . Suppose that a random mapping is uniformly distributed on . We consider a class of sets with positive densities in the set of positive integers. Le...
Gespeichert in:
| Veröffentlicht in: | Proceedings of the Steklov Institute of Mathematics 2022-03, Vol.316 (1), p.356-369 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | Let
be the semigroup of mappings of an
-element set
into itself. For a set
, denote by
the family of those mappings in
whose component sizes belong to
. Suppose that a random mapping
is uniformly distributed on
. We consider a class of sets
with positive densities in the set
of positive integers. Let
be the number of components of the random mapping
. We find asymptotic formulas for the expectation and variance of the random variable
as
. |
|---|---|
| ISSN: | 0081-5438 1531-8605 |
| DOI: | 10.1134/S0081543822010242 |