Geodesic
Generating countable sets of surjective functions
J. D. Mitchell1 ; Y. Péresse1
1 Mathematical Institute North Haugh St Andrews, Fife, KY16 9SS, Scotland
Fundamenta Mathematicae, Tome 213 (2011) no. 1, pp. 67-93

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

We prove that any countable set of surjective functions on an infinite set of cardinality $\aleph_n$ with $n\in\mathbb N$ can be generated by at most $n^2/2+9n/2+7$ surjective functions of the same set; and there exist $n^2/2+9n/2+7$ surjective functions that cannot be generated by any smaller number of surjections. We also present several analogous results for other classical infinite transformation semigroups such as the injective functions, the Baer–Levi semigroups, and the Schützenberger monoids.
DOI : 10.4064/fm213-1-4
Keywords: prove countable set surjective functions infinite set cardinality aleph mathbb generated surjective functions set there exist surjective functions cannot generated smaller number surjections present several analogous results other classical infinite transformation semigroups injective functions baer levi semigroups sch tzenberger monoids

J. D. Mitchell 1 ; Y. Péresse 1

1 Mathematical Institute North Haugh St Andrews, Fife, KY16 9SS, Scotland 
@article{10_4064_fm213_1_4,
     author = {J. D. Mitchell and Y. P\'eresse},
     title = {Generating countable sets of surjective functions},
     journal = {Fundamenta Mathematicae},
     pages = {67--93},
     publisher = {mathdoc},
     volume = {213},
     number = {1},
     year = {2011},
     doi = {10.4064/fm213-1-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm213-1-4/}
}
TY  - JOUR
AU  - J. D. Mitchell
AU  - Y. Péresse
TI  - Generating countable sets of surjective functions
JO  - Fundamenta Mathematicae
PY  - 2011
SP  - 67
EP  - 93
VL  - 213
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm213-1-4/
DO  - 10.4064/fm213-1-4
LA  - en
ID  - 10_4064_fm213_1_4
ER  - 
%0 Journal Article
%A J. D. Mitchell
%A Y. Péresse
%T Generating countable sets of surjective functions
%J Fundamenta Mathematicae
%D 2011
%P 67-93
%V 213
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm213-1-4/
%R 10.4064/fm213-1-4
%G en
%F 10_4064_fm213_1_4
J. D. Mitchell; Y. Péresse. Generating countable sets of surjective functions. Fundamenta Mathematicae, Tome 213 (2011) no. 1, pp. 67-93. doi: 10.4064/fm213-1-4

Cité par Sources :