Enumerating meandric systems with large number of loops
Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 4, pp. 607-640.
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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 points with loops in terms of a finite (the size depends on ) 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 , as well as the asymptotic behavior of the meandric numbers for general .
Accepté le :
Publié le :
DOI : 10.4171/aihpd/80
Publié le :
DOI : 10.4171/aihpd/80
Classification :
05-XX, 46-XX
Mots-clés : Meander, meandric system, free probability, free cumulant
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://archive.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://archive.numdam.org/articles/10.4171/aihpd/80/ DO - 10.4171/aihpd/80 LA - en ID - AIHPD_2019__6_4_607_0 ER -
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://archive.numdam.org/articles/10.4171/aihpd/80/
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