Geodesic
D sets and IP rich sets in $\mathbb {Z}$
Randall McCutcheon1 ; Jee Zhou1
1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A.
Fundamenta Mathematicae, Tome 233 (2016) no. 1, pp. 71-82.

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

We give combinatorial characterizations of $\mathrm {IP}$ rich sets ($\mathrm {IP}$ sets that remain $\mathrm {IP}$ upon removal of any set of zero upper Banach density) and D sets (members of idempotent ultrafilters, all of whose members have positive upper Banach density) in $\mathbb Z$. We then show that the family of $\mathrm {IP}$ rich sets strictly contains the family of D sets.
DOI : 10.4064/fm950-11-2015
Keywords: combinatorial characterizations mathrm rich sets mathrm sets remain mathrm removal set zero upper banach density sets members idempotent ultrafilters whose members have positive upper banach density mathbb family mathrm rich sets strictly contains family sets

Randall McCutcheon 1 ; Jee Zhou 1

1 Department of Mathematical Sciences University of Memphis Memphis, TN 38152, U.S.A. 
@article{10_4064_fm950_11_2015,
     author = {Randall McCutcheon and Jee Zhou},
     title = {D sets and {IP} rich sets in $\mathbb {Z}$},
     journal = {Fundamenta Mathematicae},
     pages = {71--82},
     publisher = {mathdoc},
     volume = {233},
     number = {1},
     year = {2016},
     doi = {10.4064/fm950-11-2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm950-11-2015/}
}
TY  - JOUR
AU  - Randall McCutcheon
AU  - Jee Zhou
TI  - D sets and IP rich sets in $\mathbb {Z}$
JO  - Fundamenta Mathematicae
PY  - 2016
SP  - 71
EP  - 82
VL  - 233
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm950-11-2015/
DO  - 10.4064/fm950-11-2015
LA  - en
ID  - 10_4064_fm950_11_2015
ER  - 
%0 Journal Article
%A Randall McCutcheon
%A Jee Zhou
%T D sets and IP rich sets in $\mathbb {Z}$
%J Fundamenta Mathematicae
%D 2016
%P 71-82
%V 233
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm950-11-2015/
%R 10.4064/fm950-11-2015
%G en
%F 10_4064_fm950_11_2015
Randall McCutcheon; Jee Zhou. D sets and IP rich sets in $\mathbb {Z}$. Fundamenta Mathematicae, Tome 233 (2016) no. 1, pp. 71-82. doi : 10.4064/fm950-11-2015. http://geodesic.mathdoc.fr/articles/10.4064/fm950-11-2015/

Cité par Sources :