Domination; Independent domination; Matching; 2-Satisfiability

For some finite set A of points in Rn and some integer k∈N we consider the problem of reconstructing the set A up to isometry from the multiset of the (|A|k) subsets of A of cardinality k given up to isometry. We prove the best possible result for n=1 and settle an open problem for n=2 mentioned by Krasikov and Roditty in (Ars Combin. 25B (1988) 211–219).