## Abstract

IP* sets and central sets are subsets of ℕ which arise out of applications of topological dynamics to number theory and are known to have rich combinatorial structure. Spectra of numbers are often studied sets of the form {[nα + γ] : n ∈ ℕ}. Iterated spectra are similarly defined with n coming from another spectrum. Using elementary, dynamical, and algebraic approaches we show that iterated spectra have significantly richer combinatorial structure than was previously known. For example we show that if α > 0 and 0 < γ γ 1, then {[nα + γ]: n ∈ ℕ} is an IP* set and consequently contains an infinite sequence together with all finite sums and products of terms from that sequence without repetition.

Original language | English (US) |
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Pages (from-to) | 893-912 |

Number of pages | 20 |

Journal | Transactions of the American Mathematical Society |

Volume | 348 |

Issue number | 3 |

DOIs | |

State | Published - 1996 |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics