Open AccessPermutations that preserve asymptotically null sets and statistical convergence
Author(s) -
Jeff Connor
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2014821c
Subject(s) - mathematics , permutation (music) , natural density , combinatorics , zero (linguistics)
The main result of this article is a characterization of the permutations ?: N ? N that map a set with zero asymptotic density into a set with zero asymptotic density; a permutation has this property if and only if the lower asymptotic density of Cp tends to 1 as p ? ? where p is an arbitrary natural number and Cp = {l : ?-1(l)? lp}. We then show that a permutation has this property if and only if it maps statistically convergent sequences into statistically convergent sequences.