### Abstract

For a set A of non-negative numbers, let D(A) (the difference set of A) be the set of non-negative differences of elements of A, and let D^{k} be the k-fold iteration of D. We show that for every k, almost every set of non-negative integers containing 0 arises as D^{k} (A) for some A. We also give sufficient conditions for a set A to be the unique set Χ such that 0 ∈ Χ and D^{k} (Χ)=D^{k} (A). We show that for each m there is a set A such that D(Χ)=D(A) has exactly 2^{m} solutions Χ with 0∈Χ.

Original language | English |
---|---|

Pages (from-to) | 87-106 |

Number of pages | 20 |

Journal | Combinatorica |

Volume | 16 |

Issue number | 1 |

Publication status | Published - 1996 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Discrete Mathematics and Combinatorics

### Cite this

*Combinatorica*,

*16*(1), 87-106.

**Difference sets and inverting the difference operator.** / Füredi, Z.; Jockusch, Carl G.; Rubel, Lee A.

Research output: Contribution to journal › Article

*Combinatorica*, vol. 16, no. 1, pp. 87-106.

}

TY - JOUR

T1 - Difference sets and inverting the difference operator

AU - Füredi, Z.

AU - Jockusch, Carl G.

AU - Rubel, Lee A.

PY - 1996

Y1 - 1996

N2 - For a set A of non-negative numbers, let D(A) (the difference set of A) be the set of non-negative differences of elements of A, and let Dk be the k-fold iteration of D. We show that for every k, almost every set of non-negative integers containing 0 arises as Dk (A) for some A. We also give sufficient conditions for a set A to be the unique set Χ such that 0 ∈ Χ and Dk (Χ)=Dk (A). We show that for each m there is a set A such that D(Χ)=D(A) has exactly 2m solutions Χ with 0∈Χ.

AB - For a set A of non-negative numbers, let D(A) (the difference set of A) be the set of non-negative differences of elements of A, and let Dk be the k-fold iteration of D. We show that for every k, almost every set of non-negative integers containing 0 arises as Dk (A) for some A. We also give sufficient conditions for a set A to be the unique set Χ such that 0 ∈ Χ and Dk (Χ)=Dk (A). We show that for each m there is a set A such that D(Χ)=D(A) has exactly 2m solutions Χ with 0∈Χ.

UR - http://www.scopus.com/inward/record.url?scp=0040523126&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040523126&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 87

EP - 106

JO - Combinatorica

JF - Combinatorica

SN - 0209-9683

IS - 1

ER -