A combinatorial interpretation for two transformations of series that commute with compositional inversion |
| |
Authors: | Robert Donaghey |
| |
Institution: | Department of Mathematics, Baruch College, CUNY, New York, New York 10010 USA |
| |
Abstract: | For a formal power series with nonnegative integer coefficients, the compositional inverse of is shown to be the generating function for the colored planted plane trees in which each vertex of degree i + 1 is colored one of hi colors. Since the compositional inverse of the Euler transformation of f(t) is the star transformation g(t)]?1 ? 1]?1 of g(t), 2], it follows that the Euler transformation of f(t) is the generating function for the colored planted plane trees in which each internal vertex of degree i + 1 is colored one of hi colors for i > 1, and h1 ? 1 colors for i = 1. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|