The Distribution of Heights of Binary Trees and Other Simple Trees
1993 ◽
Vol 2
(2)
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pp. 145-156
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Keyword(s):
The number, , of rooted plane binary trees of height ≤ h with n internal nodes is shown to satisfyuniformly for δ−1(log n)−1/2 ≤ β ≤ δ(log n)1/2, where and δ is a positive constant. An asymptotic formula for is derived for h = cn, where 0 < c < 1. Bounds for are also derived for large and small heights. The methods apply to any simple family of trees, and the general asymptotic results are stated.
1956 ◽
Vol 52
(1)
◽
pp. 49-60
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1966 ◽
Vol 62
(4)
◽
pp. 637-642
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Keyword(s):
Keyword(s):
1991 ◽
Vol 43
(1)
◽
pp. 182-212
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1992 ◽
Vol 35
(1)
◽
pp. 121-131
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2017 ◽
Vol 153
(8)
◽
pp. 1622-1657
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2014 ◽
Vol 144
(4)
◽
pp. 819-829
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Keyword(s):
1998 ◽
Vol 50
(3)
◽
pp. 563-580
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