Enumerating meandric systems with large number of loops
Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 4, pp. 607-640.

We investigate meandric systems with a large number of loops using tools inspired by free probability. For any fixed integer r, we express the generating function of meandric systems on 2n points with n→r loops in terms of a finite (the size depends on r) subclass of irreducible meandric systems, via the moment-cumulant formula from free probability theory. We show that the generating function, after an appropriate change of variable, is a rational function, and we bound its degree. Exact expressions for the generating functions are obtained for r≤6, as well as the asymptotic behavior of the meandric numbers for general r.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/80
Classification : 05-XX, 46-XX
Mots-clés : Meander, meandric system, free probability, free cumulant 
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Fukuda, Motohisa; Nechita, Ion. Enumerating meandric systems with large number of loops. Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 4, pp. 607-640. doi : 10.4171/aihpd/80. https://www.numdam.org/articles/10.4171/aihpd/80/
  • Borga, Jacopo; Gwynne, Ewain; Park, Minjae On the Geometry of Uniform Meandric Systems, Communications in Mathematical Physics, Volume 404 (2023) no. 1, p. 439 | DOI:10.1007/s00220-023-04846-y
  • Féray, Valentin; Thévenin, Paul Components in Meandric Systems and the Infinite Noodle, International Mathematics Research Notices, Volume 2023 (2023) no. 14, p. 12538 | DOI:10.1093/imrn/rnac156

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