# Critical connectedness of thin arithmetical discrete planes

2 ADAGIO - Applying Discrete Algorithms to Genomics and Imagery
LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
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.
Domain :

https://hal.inria.fr/hal-00966947
Contributor : Xavier Provençal <>
Submitted on : Thursday, March 27, 2014 - 3:54:45 PM
Last modification on : Saturday, March 28, 2020 - 2:09:37 AM

### Identifiers

• HAL Id : hal-00966947, version 1
• ARXIV : 1312.7820

### Citation

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

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