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Chapitre D'ouvrage Année : 2015

The common structure of the curves having a same Gauss word

Résumé

Gauss words are finite sequences of letters associated with self-intersec-ting closed curves in the plane. (These curves have no "triple" self-intersection). These sequences encode the order of intersections on the curves. We characterize, up to homeomorphism, all curves having a given Gauss word. We extend this characterization to the n-tuples of closed curves having a given n-tuple of words, that we call a Gauss multiword . These words encode the self-intersections of the curves and their pairwise intersections. Our characterization uses a canonical decomposition of strongly connected graphs, called the atomic decomposition, that we have defined and studied in a previous article.
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Dates et versions

hal-00879514 , version 1 (04-11-2013)

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  • HAL Id : hal-00879514 , version 1

Citer

Bruno Courcelle. The common structure of the curves having a same Gauss word. A. Adamatzky. Automata, Computation, Universality, Springer, pp.1-37, 2015, Automata, Computation, Universality. ⟨hal-00879514⟩

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