Enumerating meandric systems with large number of loops
Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 4, pp. 607-640.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

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 
@article{AIHPD_2019__6_4_607_0,
     author = {Fukuda, Motohisa and Nechita, Ion},
     title = {Enumerating meandric systems with large number of loops},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {607--640},
     volume = {6},
     number = {4},
     year = {2019},
     doi = {10.4171/aihpd/80},
     mrnumber = {4033682},
     zbl = {1431.05006},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/aihpd/80/}
}
TY  - JOUR
AU  - Fukuda, Motohisa
AU  - Nechita, Ion
TI  - Enumerating meandric systems with large number of loops
JO  - Annales de l’Institut Henri Poincaré D
PY  - 2019
SP  - 607
EP  - 640
VL  - 6
IS  - 4
UR  - http://www.numdam.org/articles/10.4171/aihpd/80/
DO  - 10.4171/aihpd/80
LA  - en
ID  - AIHPD_2019__6_4_607_0
ER  - 
%0 Journal Article
%A Fukuda, Motohisa
%A Nechita, Ion
%T Enumerating meandric systems with large number of loops
%J Annales de l’Institut Henri Poincaré D
%D 2019
%P 607-640
%V 6
%N 4
%U http://www.numdam.org/articles/10.4171/aihpd/80/
%R 10.4171/aihpd/80
%G en
%F AIHPD_2019__6_4_607_0
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. http://www.numdam.org/articles/10.4171/aihpd/80/

Cité par Sources :