منابع مشابه
Reconstructing Subsets of Zn
In this paper we consider the problem of reconstructing a subset A ⊂ Z n , up to translation, from the collection of its subsets of size k, given up to translation (its k-deck). Results of Alon, Caro, Krasikov, and Roditty [1] show that this is possible provided k > log 2 n. Mnukhin [10] showed that every subset of Z n of size k is reconstructible from its (k − 1)-deck, provided k ≥ 4. We show ...
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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 locally finite; those which contain only finitel...
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Let G = (V; E) be a simple, undirected graph. A subset U V is odd if the subgraph of G induced by U has an odd number of edges. For a xed integer k, when does the knowledge of the family of odd subsets of V having cardinality k allow the reconstruction of G? The answer is: whenever k jV j?2 and k 2 mod 4. The proof proceeds via the vector space homomorphism k : (?(n);) ?! (? k (n);), where ?(n)...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1998
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2870