Abstract
In this part starting from a generalization of the binomial theorem a development of Rota's theory of polynomial sequences of binomial type to the case of countably many noncommuting variables is given. Translation invariance of operators gives the relation to the formal power series considered inI. For a special class of binomial systems there are given a number of characterizations, such as a generalized Rodrigues formula. In the case of an analogue of the Newton polynomials those are used for a study of generalized Stirling numbers. (In III the theory of binomial systems of diagonal type will be continued until an analogue of Lagrange inversion and a short development of the theory of generalized Sheffer polynomials will be given.)
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Literatur
Baron, G., Kirschenhofer, P.: Operatorenkalkül über freien Monoiden I: Strukturen. Mh. Math.91, 89–103 (1981).
Garsia, A. M., Joni, S. A.: A new expression for umbral operators and power series inversion. Proc. AMS64, 179–185 (1974).
Henle, M.: Binomial enumeration on dissects. Trans. AMS202, 1–39 (1975).
Hofbauer, J.: Beiträge zu Rota's Theorie der Folgen von Binomialtyp. S.-B. Österr: Akad. Wiss. Math. Nat. Kl. II/187, 437–489 (1978).
Michor, P.: Contributions to finite operator calculus in several variables. J. Comb. Inf. Syst. Sc.4, 39–65 (1979).
Roman, St. M., Rota, G.-C.: The umbral calculus. Adv. Math.27, 95–188 (1978).
Rota, G.-C., Kahaner, D., Odlyzko, A.: On the foundations of combinatorial theory VIII: Finite operator calculus. J. Math. Anal. Appl.42, 684–760 (1973).
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Baron, G., Kirschenhofer, P. Operatorenkalkül über freien Monoiden II: Binomialsysteme. Monatshefte für Mathematik 91, 181–196 (1981). https://doi.org/10.1007/BF01301786
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DOI: https://doi.org/10.1007/BF01301786