Flajolet, Philippe; Gao, Zhicheng; Odlyzko, Andrew; Richmond, Bruce The distribution of heights of binary trees and other simple trees. (English) Zbl 0795.05042 Comb. Probab. Comput. 2, No. 2, 145-156 (1993). The authors derive a local limit theorem for the distribution of the number of binary trees with \(n\) interior nodes and height \(h\), when \(\delta^{-1} (\log n)^{-1/2} \leq h/2 \sqrt n \leq \delta (\log n)^{1/2}\) for fixed \(\delta>0\). They also consider the case when \(h=cn\), where \(0<c<1\), among other things. Corresponding results for more general simply generated families of trees are also given. Reviewer: J.W.Moon (Edmonton) Cited in 16 Documents MSC: 05C05 Trees 05C30 Enumeration in graph theory 60F99 Limit theorems in probability theory Keywords:limit theorem; distribution; binary trees; height PDFBibTeX XMLCite \textit{P. Flajolet} et al., Comb. Probab. Comput. 2, No. 2, 145--156 (1993; Zbl 0795.05042) Full Text: DOI References: [1] de Bruijn, Graph Theory and Computing pp 15– (1972) · doi:10.1016/B978-1-4832-3187-7.50007-6 [2] de Bruijn, Asymptotic Methods in Analysis (1961) [3] DOI: 10.1287/moor.9.1.43 · Zbl 0529.68035 · doi:10.1287/moor.9.1.43 [4] DOI: 10.1016/0097-3165(83)90062-6 · Zbl 0511.05003 · doi:10.1016/0097-3165(83)90062-6 [5] DOI: 10.1137/0215039 · Zbl 0616.68063 · doi:10.1137/0215039 [6] DOI: 10.1016/0022-0000(82)90004-6 · Zbl 0499.68027 · doi:10.1016/0022-0000(82)90004-6 [7] DOI: 10.1007/BF02559539 · Zbl 0145.07903 · doi:10.1007/BF02559539 [8] DOI: 10.1016/0001-8708(82)90005-6 · Zbl 0484.30002 · doi:10.1016/0001-8708(82)90005-6 [9] Meir, Canad. J. Math. 30 pp 997– (1978) · Zbl 0394.05015 · doi:10.4153/CJM-1978-085-0 [10] DOI: 10.1017/S1446788700004432 · Zbl 0153.25802 · doi:10.1017/S1446788700004432 [11] DOI: 10.1016/0377-0427(91)90197-R · Zbl 0724.41030 · doi:10.1016/0377-0427(91)90197-R This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.