We give combinatorial characterizations of IP rich sets (IP sets that remain 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 ℤ. We then show that the family of IP rich sets strictly contains the family of D sets.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm950-11-2015,
author = {Randall McCutcheon and Jee Zhou},
title = {D sets and IP rich sets in $\mathbb{Z}$},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {71-82},
zbl = {06545390},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm950-11-2015}
}
Randall McCutcheon; Jee Zhou. D sets and IP rich sets in ℤ. Fundamenta Mathematicae, Tome 233 (2016) pp. 71-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm950-11-2015/