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- W2064895286 abstract "In Discrete Tomography there are two related notions of interest: H -uniqueness and H -additivity of finite subsets of N m , which are defined for certain finite sets H of linear subspaces of R m . One knows complete sets of obstructions for H -uniqueness (bad H -configurations) and for H -additivity (weakly bad H -configurations). The classical case, when H is the set of coordinate axes in R 2 , is well known. Let H m denote the set of the m coordinate hyperplanes of R m . The following question was raised in [P.C. Fishburn, J.C. Lagarias, J.A. Reeds, L.A. Shepp, Sets uniquely determined by projections on axes II. Discrete case, Discrete Math. 91 (1991) 149–159]. Is there an upper bound on the weights of the bad H m -configurations one needs to consider to determine H m -uniqueness ( m ≥ 3 ) of an arbitrary set in N m ? This question can be asked for other sets H of linear subspaces and also for H -additivity. The answer to this question, in the case of uniqueness, is known when H is a set of lines. In this paper we answer this question for uniqueness and additivity in the case of H 3 . We show that there is no upper bound on the weights of the bad configurations (resp. weakly bad configurations) one needs to consider to determine H 3 -uniqueness (resp. H 3 -additivity)." @default.
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- W2064895286 date "2008-10-01" @default.
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- W2064895286 title "Additivity obstructions for integral matrices and pyramids" @default.
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- W2064895286 doi "https://doi.org/10.1016/j.tcs.2008.06.004" @default.
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