A combinatorial interpretation for the Schett recurrence on the Jacobian elliptic functions
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- by Dominique Dumont PDF
- Math. Comp. 33 (1979), 1293-1297 Request permission
Abstract:
The coefficients introduced by Alois Schett containing the Taylor series expansions of the Jacobian elliptic functions are proved to count certain classes of permutations.References
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D. ANDRE, "Développement de $\sec x$ et $\tan x$," C. R. Acad. Sci. Paris, v. 88, 1879, pp. 965-967.
D. FOATA & M. P. SCHÜTZENBERGER, Théorie Géométrique des Polynômes Eulériens, Lecture Notes in Math., Vol. 138, Springer-Verlag, Berlin and New York, 1970.
- Alois Schett, Properties of the Taylor series expansion coefficients of the Jacobian elliptic functions, Math. Comp. 30 (1976), no. 133, 143–147. MR 391477, DOI 10.1090/S0025-5718-1976-0391477-3 A. SCHETT, Addendum to "Properties of the Taylor series expansion coefficients of the Jacobian elliptic functions," Math. Comp., v. 31, 1977, Microfiche supplement.
- Alois Schett, Recurrence formula of the Taylor series expansion coefficients of the Jacobian elliptic functions, Math. Comp. 31 (1977), no. 140, 1003–1005. MR 442301, DOI 10.1090/S0025-5718-1977-0442301-2
- Gérard Viennot, Une interprétation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi, J. Combin. Theory Ser. A 29 (1980), no. 2, 121–133 (French, with English summary). MR 583951, DOI 10.1016/0097-3165(80)90001-1
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Math. Comp. 33 (1979), 1293-1297
- MSC: Primary 33A25; Secondary 05A15
- DOI: https://doi.org/10.1090/S0025-5718-1979-0537974-1
- MathSciNet review: 537974