## Mathematics, Department of

#### Date of this Version

1999

#### Citation

The Electronic Journal of Combinatorics 6

#### Abstract

We consider the problem of reconstructing a set of real numbers up to translation from the multiset of its subsets of fixed size, given up to translation. This is impossible in general: for instance almost all subsets of Z contain infinitely many translates of every finite subset of Z. We therefore restrict our attention to subsets of R which are *locally finite*; those which contain only finitely many translates of any given finite set of size at least 2. We prove that every locally finite subset of R is reconstructible from the multiset of its 3-subsets, given up to translation

## Comments

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