Difference sets and inverting the difference operator

Z. Füredi, Carl G. Jockusch, Lee A. Rubel

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)87-106
Number of pages20
JournalCombinatorica
Volume16
Issue number1
Publication statusPublished - 1996

Fingerprint

Difference Set
Difference Operator
Non-negative
Fold
Iteration
Integer
Sufficient Conditions

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics

Cite this

Füredi, Z., Jockusch, C. G., & Rubel, L. A. (1996). Difference sets and inverting the difference operator. Combinatorica, 16(1), 87-106.

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

In: Combinatorica, Vol. 16, No. 1, 1996, p. 87-106.

Research output: Contribution to journalArticle

Füredi, Z, Jockusch, CG & Rubel, LA 1996, 'Difference sets and inverting the difference operator', Combinatorica, vol. 16, no. 1, pp. 87-106.
Füredi, Z. ; Jockusch, Carl G. ; Rubel, Lee A. / Difference sets and inverting the difference operator. In: Combinatorica. 1996 ; Vol. 16, No. 1. pp. 87-106.
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