Article contents
A Formal Solution of Σ∞i=1AieBix = X
Published online by Cambridge University Press: 20 November 2018
Extract
We consider a combinatorial enumeration problem involving certain collections of labelled rooted trees having coloured nodes and edges. Notations and definitions are introduced in §§2 and 3, and the problem is described in §4. We give recursion formulas for its solution in §5. Then, by using a modification of a method of Priifer, we obtain a direct solution in terms of multinomial coefficients and power products in §§6 and 7. These results are combined in §8. Working in a formal power series algebra we find a formal solution of the equation
which expresses the unknown X as a multiple power series in the Ai and the Bi.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1964
References
- 5
- Cited by