Horibe, Yasuichi Entropy of terminal distributions and the Fibonacci trees. (English) Zbl 0646.05002 Fibonacci Q. 26, No. 2, 135-140 (1988). 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 \((p,\bar p)\)-assigned Fibonacci tree \(T_ k\) is given by \[ H_ k=\frac{(p,\bar p)}{2-p}\{(k-2)\frac{\bar p+(-p)^{k-1}}{1+\bar p}\},\quad k\geq 3. \] Reviewer: G.Philippou Cited in 1 ReviewCited in 1 Document MSC: 05A15 Exact enumeration problems, generating functions 11B37 Recurrences Keywords:binary tree; c-minimal; Fibonacci trees; entropy; terminal distribution Citations:Zbl 0491.94009; Zbl 0512.05003 PDFBibTeX XMLCite \textit{Y. Horibe}, Fibonacci Q. 26, No. 2, 135--140 (1988; Zbl 0646.05002)