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Number of circle graphs of Gauss diagrams of meander curves with 2n+1 crossings.
0

%I #20 Dec 30 2021 00:24:07

%S 1,2,5,13,43,167

%N Number of circle graphs of Gauss diagrams of meander curves with 2n+1 crossings.

%C See A343358 for a definition of a graph corresponding to a closed planar curve. Meanders have been defined in various ways; for the purpose of considering their Gauss diagrams and graphs, a meander is understood as a closed planar curve in whose graph there is a vertex adjacent to every other vertex. This sequence is the number of distinct graphs of meanders of (necessarily odd) sizes.

%D Delecroix, Vincent, et al. "Enumeration of meanders and Masur-Veech volumes." Forum of Mathematics, Pi. Vol. 8. Cambridge University Press, 2020.

%D Grinblat, Andrey, and Viktor Lopatkin. "On realizabilty of Gauss diagrams and constructions of meanders." Journal of Knot Theory and Its Ramifications 29.05 (2020): 2050031.

%H V. Delecroix et al. <a href="https://arxiv.org/abs/1705.05190">Enumeration of meanders and Masur-Veech volumes</a>, arXiv preprint arXiv:1705.05190 [math.GT], 2017-2019.

%H Andrey Grinblat and Viktor Lopatkin. <a href="https://arxiv.org/abs/1808.08542">On realizabilty of Gauss diagrams and constructions of meanders.</a> arXiv:1808.08542 [math.AT], 2018.

%H Abdullah Khan, Alexei Lisitsa, Viktor Lopatkin, and Alexei Vernitski, <a href="https://arxiv.org/abs/2108.02873">Circle graphs (chord interlacement graphs) of Gauss diagrams: Descriptions of realizable Gauss diagrams, algorithms, enumeration</a>, arXiv:2108.02873 [math.GT], 2021.

%Y Cf. A343358.

%K nonn,hard,more

%O 1,2

%A _Alexei Vernitski_, Apr 22 2021