Reconstructing subsets of reals
The electronic journal of combinatorics, Tome 6 (1999)
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 $\mathbb{Z}$ contain infinitely many translates of every finite subset of $\mathbb{Z}$. We therefore restrict our attention to subsets of $\mathbb{R}$ 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 $\mathbb{R}$ is reconstructible from the multiset of its 3-subsets, given up to translation.
DOI :
10.37236/1452
Classification :
05A99, 05C60
Mots-clés : reconstruction, \(k\)-orbits, \(k\)-deck, subsets
Mots-clés : reconstruction, \(k\)-orbits, \(k\)-deck, subsets
@article{10_37236_1452,
author = {A. J. Radcliffe and A. D. Scott},
title = {Reconstructing subsets of reals},
journal = {The electronic journal of combinatorics},
year = {1999},
volume = {6},
doi = {10.37236/1452},
zbl = {0914.05005},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1452/}
}
A. J. Radcliffe; A. D. Scott. Reconstructing subsets of reals. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1452
Cité par Sources :