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D sets and IP rich sets in $\mathbb {Z}$

Tom 233 / 2016

Randall McCutcheon, Jee Zhou Fundamenta Mathematicae 233 (2016), 71-82 MSC: Primary 22A15; Secondary 05D10. DOI: 10.4064/fm950-11-2015 Opublikowany online: 25 November 2015

Streszczenie

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.

Autorzy

  • Randall McCutcheonDepartment of Mathematical Sciences
    University of Memphis
    Memphis, TN 38152, U.S.A.
    e-mail
  • Jee ZhouDepartment of Mathematical Sciences
    University of Memphis
    Memphis, TN 38152, U.S.A.
    e-mail

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