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Minimal arithmetic thickness connecting discrete planes

Abstract : While connected arithmetic discrete lines are entirely characterized, only partial results exist for the more general case of arithmetic discrete hyperplanes. In the present paper, we focus on the $3$-dimensional case, that is on arithmetic discrete planes. Thanks to arithmetic reductions on a vector $\vect{n}$, we provide algorithms either to determine whether a given arithmetic discrete plane with $\vect{n}$ as normal vector is connected, or to compute the minimal thickness for which an arithmetic discrete plane with normal vector $\vect{n}$ is connected.
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https://hal.archives-ouvertes.fr/hal-00579872
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Damien Jamet, Jean-Luc Toutant. Minimal arithmetic thickness connecting discrete planes. Discrete Applied Mathematics, Elsevier, 2009, 157 (3), pp.500-509. ⟨10.1016/j.dam.2008.05.027⟩. ⟨hal-00579872⟩

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