A338660 Number of circle graphs of Gauss diagrams of meander curves with 2n+1 crossings.

1, 2, 5, 13, 43, 167

Offset

1,2

Comments

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.

References

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

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.

Links

Table of n, a(n) for n=1..6.

V. Delecroix et al. Enumeration of meanders and Masur-Veech volumes, arXiv preprint arXiv:1705.05190 [math.GT], 2017-2019.

Andrey Grinblat and Viktor Lopatkin. On realizabilty of Gauss diagrams and constructions of meanders. arXiv:1808.08542 [math.AT], 2018.

Abdullah Khan, Alexei Lisitsa, Viktor Lopatkin, and Alexei Vernitski, Circle graphs (chord interlacement graphs) of Gauss diagrams: Descriptions of realizable Gauss diagrams, algorithms, enumeration, arXiv:2108.02873 [math.GT], 2021.

Crossrefs

Cf. A343358.

Sequence in context: A307263 A278171 A212824 * A286949 A287023 A287008

Adjacent sequences: A338657 A338658 A338659 * A338661 A338662 A338663

Keyword

nonn,hard,more

Author

Alexei Vernitski, Apr 22 2021

Status

approved