Abstract
Gauss words are finite sequences of letters associated with self-intersecting 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 decompositions of strongly connected graphs in 3-edge-connected components and algebraic terms formalizing these decompositions.
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Courcelle, B. (2015). The Common Structure of the Curves Having a Same Gauss Word. In: Adamatzky, A. (eds) Automata, Universality, Computation. Emergence, Complexity and Computation, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-09039-9_1
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DOI: https://doi.org/10.1007/978-3-319-09039-9_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09038-2
Online ISBN: 978-3-319-09039-9
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