Abstract:It is shown here the compositional inversion of formal power series has a natural formulation in terms of umbral operators. This fact is used to derive a new proof of the Lagrange inversion theorem by operator theoretic methods.
- Adriano M. Garsia, An exposé of the Mullin-Rota theory of polynomials of binomial type, Linear and Multilinear Algebra 1 (1973), no. 1, 47–65. MR 319779, DOI 10.1080/03081087308817005
- Ronald Mullin and Gian-Carlo Rota, On the foundations of combinatorial theory. III. Theory of binomial enumeration, Graph Theory and its Applications (Proc. Advanced Sem., Math. Research Center, Univ. of Wisconsin, Madison, Wis., 1969) Academic Press, New York, 1970, pp. 167–213 (loose errata). MR 0274300
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 64 (1977), 179-185
- MSC: Primary 05A10; Secondary 40A99
- DOI: https://doi.org/10.1090/S0002-9939-1977-0444487-4
- MathSciNet review: 0444487