Stanley, R. P. Differentiably finite power series. (English) Zbl 0445.05012 Eur. J. Comb. 1, 175-188 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 133 Documents MSC: 05A15 Exact enumeration problems, generating functions 34K05 General theory of functional-differential equations 05-02 Research exposition (monographs, survey articles) pertaining to combinatorics Keywords:formal power series; differentiably finite; reciprocity theorems; p- recursive; d-finite PDF BibTeX XML Cite \textit{R. P. Stanley}, Eur. J. Comb. 1, 175--188 (1980; Zbl 0445.05012) Full Text: DOI OpenURL References: [1] Anand, H.; Dumir, V.C.; Gupta, H., A combinatorial distribution problem, Duke math. J., 33, 757-769, (1966) · Zbl 0144.00401 [2] R. P. Brent and H. T. Kung, Fast algorithms for manipulating formal power series, J. Assoc. Comp. Mach., (to appear). · Zbl 0388.68052 [3] Brent, R.P.; Traub, J.F., On the complexity of composition and generalized composition of power series, Dept. of computer science report, (1978), Carnegie-Mellon Univ · Zbl 0447.68033 [4] Carlitz, L., Recurrences for Bernoulli and Euler numbers, J. reine angew. math, 214/215, 184-191, (1964) · Zbl 0126.26204 [5] Chung, F.R.K.; Graham, R.L.; Hoggatt, V.E.; Kleiman, M., The number of Baxter permutations, J. combinatorial theory, 24, A, 382-394, (1978) · Zbl 0398.05003 [6] Cohn, P.M., Algebra and language theory, Bull. London math. soc., 7, 1-29, (1975) · Zbl 0314.68032 [7] Comtet, L., Calcul pratique des coefficients de Taylor d’une fonction algébrique, Enseignement math., 10, 267-270, (1964) · Zbl 0166.41702 [8] Comtet, L., Advanced combinatorics, (1974), Reidel Dordrecht and Boston [9] Fliess, M., Sur divers produits de séries formelles, Bull. soc. math. France, 102, 181-191, (1974) · Zbl 0313.13021 [10] Franel, J., L’intermédiaire des mathématiciens 1 (1894), 45-47;, 2, 33-35, (1895) [11] Furstenberg, H., Algebraic function fields over finite fields, J. algebra, 7, 271-277, (1967) · Zbl 0175.03903 [12] Gupta, H., Enumeration of symmetric matrices, Duke math. J., 35, 653-659, (1968) · Zbl 0185.03401 [13] Jungen, R., Sur LES séries de Taylor n’ayant que des singularités algébrao-logarithmiques sur leur cercle de convergence, Comment. math. helv., 3, 266-306, (1931) · JFM 57.0373.03 [14] Katz, M., On the extreme points of a certain convex polytope, J. combinatorial theory, 8, 417-423, (1970) · Zbl 0194.34102 [15] Katz, M., On the extreme points of the set of substochastic and symmetric matrices, J. math. anal. appl., 37, 576-579, (1972) · Zbl 0235.15007 [16] Kung, H.T.; Traub, J.F., All algebraic functions can be computed fast, J. assoc. comp. Mach., 25, 245-260, (1978) · Zbl 0371.68019 [17] Pólya, G.; Szegö, G., () [18] Popoviciu, T., Studie si cercetari stiintifice, Acad. R.P.R. filiala cluj, 4, 8, (1953) [19] Read, R.C., The enumeration of locally restricted graphs (II), J. London math. soc., 35, 344-351, (1960) · Zbl 0209.55501 [20] Read, R.C., Some unusual enumeration problems, Ann. New York acad. sci., 175, 314-326, (1970) · Zbl 0225.05111 [21] A. Regev, Asymptotic values for degrees associated with strips of Young diagrams, preprint. · Zbl 0509.20009 [22] Stanley, R.P., Generating functions, MAA studies in combinatorics, (), 100-141 [23] van der Poorten, A., A proof that Euler missed ... apéry’s proof of the irrationality of C(3), Math. intelligencer, 1, 195-203, (1979) · Zbl 0409.10028 [24] D. Zeilberger, The algebra of linear partial difference operators and its applications, preprint. · Zbl 0458.39002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.