Elliptic functions, continued fractions and doubled permutations
type: Item
instance of: scholarly article
title: Elliptic functions, continued fractions and doubled permutations
zbMATH Open document ID: 0681.05002
DOI: 10.1016/S0195-6698(89)80057-5
author: Philippe Flajolet
author: Jean Francon
published in: European Journal of Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: In this paper it is shown that the coefficients in the Taylor expansion of the elliptic function sn(z,\(\alpha)\) count the number of odd doubled permutations of 1 to \(2n+1\) having \(2k+1\) falls, and a similar result for the function cn(z,\(\alpha)\). (A doubled permutation is one such that, for each i, \(2i+1\) and \(2\sigma +2\) are of the same ordered type, of which there are four, namely `peak', `valley', `double rise' and `double fall'). The proof uses the continued fraction expansions of the Laplace transforms of sn(2,\(\alpha)\) and cn(2,\(\alpha)\), and properties of path diagrams.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 33E05
zbMATH DE Number: 4114634
zbMATH Keywords: elliptic function
zbMATH Keywords: doubled permutations
zbMATH Keywords: continued fraction
reviewed by: Ronald C. Read
MaRDI profile type: Publication
cites work: Permutations, Sequences and Special Functions
cites work: Q5625163
cites work: A Combinatorial Interpretation for the Schett Recurrence on the Jacobian Elliptic Functions
cites work: Q5820721
cites work: Combinatorial aspects of continued fractions
cites work: Permutations selon leurs pics, creux, doubles montees et double descentes, nombres d'Euler et nombres de Genocchi
cites work: Q3244409
cites work: Distributions, continued fractions, and the Ehrenfest urn model
cites work: Path generating functions and continued fractions
cites work: Q3669422
cites work: Some results on ''product-weighted lead codes''
cites work: Combinatoire énumérative. Proceedings of the ''Colloque de combinatoire énumérative'' (Colloquium on Enumerative Combinatorics), held at Université du Québec à Montréal (Canada), May 28 - June 1, 1985
cites work: Sur Un Problème De Configurations Et Sur Les Fractions Continues
cites work: Une interpretation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi
cites work: Q3676951
description: scientific article; zbMATH DE number 4114634