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Additivity Obstructions for Integral Matrices and Pyramids by Miguel Santoyo; Ernesto Vallejo is a Computer Science article available to read on EtoBox.
What is Additivity Obstructions for Integral Matrices and Pyramids about?
In Discrete Tomography there are two related notions of interest: H-uniqueness and Hadditivity 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 Hconfigurations) 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 configurat
Who reads Additivity Obstructions for Integral Matrices and Pyramids?
It is typically read by researchers, students, and practitioners in Computer Science.
- Author
- Miguel Santoyo; Ernesto Vallejo
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0304-3975)
- Published
- 2008
- Language
- EN
- Field
- Computer Science (Physical Sciences)