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On functional equations arising from map enumerations

✍ Scribed by Yanpei Liu

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 911 KB
Volume: 123
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90009-i

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✦ Synopsis

This paper summarizes with a number of new results, a variety of functional equations which arise from the enumerations of planar maps. A few applications are also discussed.

We usually write X=X,, s(X) when it is not necessary to notify X, a and p.

Condition 2. The permutation f on X has to obey the following two axioms.

Axiom 1. ccf=b-lx.

Axiom 2. The group YJ generated by J = { c(, /3,2} is transitive on X.

Thus, we may write the map M = (X,,,(X), f). From Axiom 1, CI, /3 are asymmetric, i.e. (Xm,,(X),y)#(X,,.(X),y). Generally, for a map M=(X&X),y), it is not necessary that (X,,,(X),,$) is also a map because for fi, it is not guaranteed to have

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