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{\bf A.~J.~Radcliffe and A.~D.~Scott}
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{\bf Reconstructing Subsets of Reals}
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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 
{\it 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.



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