Geodesic
The prevalence of permutations with infinite cycles
Fundamenta Mathematicae, Tome 144 (1994) no. 1, pp. 89-94

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A number of recent papers have been devoted to the study of prevalence, a generalization of the property of being of full Haar measure to topological groups which need not have a Haar measure, and the dual concept of shyness. These concepts give a notion of "largeness" which often differs from the category analogue, comeagerness, and may be closer to the intuitive notion of "almost everywhere." In this paper, we consider the group of permutations of natural numbers. Here, in the sense of category, "almost all" permutations have only finite cycles. In contrast, we show that, in terms of prevalence, "almost all" permutations have infinitely many infinite cycles and only finitely many finite cycles; this set of permutations comprises countably many conjugacy classes, each of which is non-shy.
DOI : 10.4064/fm_1994_144_1_1_89_94

Randall Dougherty 1 ; Jan Mycielski 1

1 
@article{10_4064_fm_1994_144_1_1_89_94,
     author = {Randall Dougherty and Jan Mycielski},
     title = {The prevalence of permutations with infinite cycles},
     journal = {Fundamenta Mathematicae},
     pages = {89--94},
     publisher = {mathdoc},
     volume = {144},
     number = {1},
     year = {1994},
     doi = {10.4064/fm_1994_144_1_1_89_94},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm_1994_144_1_1_89_94/}
}
TY  - JOUR
AU  - Randall Dougherty
AU  - Jan Mycielski
TI  - The prevalence of permutations with infinite cycles
JO  - Fundamenta Mathematicae
PY  - 1994
SP  - 89
EP  - 94
VL  - 144
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm_1994_144_1_1_89_94/
DO  - 10.4064/fm_1994_144_1_1_89_94
LA  - en
ID  - 10_4064_fm_1994_144_1_1_89_94
ER  - 
%0 Journal Article
%A Randall Dougherty
%A Jan Mycielski
%T The prevalence of permutations with infinite cycles
%J Fundamenta Mathematicae
%D 1994
%P 89-94
%V 144
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm_1994_144_1_1_89_94/
%R 10.4064/fm_1994_144_1_1_89_94
%G en
%F 10_4064_fm_1994_144_1_1_89_94
Randall Dougherty; Jan Mycielski. The prevalence of permutations with infinite cycles. Fundamenta Mathematicae, Tome 144 (1994) no. 1, pp. 89-94. doi: 10.4064/fm_1994_144_1_1_89_94

Cité par Sources :