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Critical connectedness of thin arithmetical discrete planes

Abstract

The critical thickness of an arithmetical discrete plane refers to the infimum thickness that preserves its $2$-connectedness. This infimum thickness can be computed thanks to a multidimensional continued fraction algorithm, namely the fully subtractive algorithm. We provide a characterization of the discrete planes with critical thickness that contain the origin and that are $2$-connected.

Dates and versions

hal-00966947 , version 1 (27-03-2014)

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Valérie Berthé, Damien Jamet, Timo Jolivet, Xavier Provençal. Critical connectedness of thin arithmetical discrete planes. 2013. ⟨hal-00966947⟩
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