D sets and IP rich sets in Z
We give combinatorial characterizations of IP rich sets (IP sets that re- main IP upon removal of any set of zero upper Banach density) and D sets (members of idempotent ultra filters, 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.
McCutcheon, R., & Zhou, J. (2016). D sets and IP rich sets in Z. Fundamenta Mathematicae, 233 (1), 71-82. https://doi.org/10.4064/fm950-11-2015