### Abstract

The uniqueness problem is considered when binary matrices are to be reconstructed from their absorbed row and column sums. Let the absorption coefficient μ be selected such that e^{μ}=(1+5)/2. Then it is proved that if a binary matrix is non-uniquely determined, then it contains a special pattern of 0s and 1s called composition of alternatively corner-connected components. In a previous paper [Discrete Appl. Math. (submitted)] we proved that this condition is also sufficient, i.e., the existence of such a pattern in the binary matrix is necessary and sufficient for its non-uniqueness.

Original language | English |
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Pages (from-to) | 171-194 |

Number of pages | 24 |

Journal | Linear Algebra and Its Applications |

Volume | 339 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Dec 15 2001 |

### Keywords

- Discrete tomography
- Projections with absorption
- Reconstruction

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

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## Cite this

Kuba, A., & Nivat, M. (2001). Reconstruction of discrete sets with absorption.

*Linear Algebra and Its Applications*,*339*(1-3), 171-194. https://doi.org/10.1016/S0024-3795(01)00486-4