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Entropy of terminal distributions and the Fibonacci trees. (English) Zbl 0646.05002

This is a continuation of two previous papers by the same author [ibid. 20, 168-178 (1982; Zbl 0491.94009) and 21, 118-128 (1983; Zbl 0512.05003)]. Presently, it is shown that under appropriate conditions a binary tree is c-minimal if and only if it is p-maximal. This principle is next used to extend some earlier findings on Fibonacci trees. It is further found that the entropy H k of the terminal distribution of the (p,p ¯)-assigned Fibonacci tree T k is given by

H k =(p,p ¯) 2-p{(k-2)p ¯+(-p) k-1 1+p ¯},k3·

Reviewer: G.Philippou

MSC:
05A15Exact enumeration problems, generating functions
11B37Recurrences