Geodesic
Some estimates for the distribution of the height of a tree for digital searching
Diskretnaya Matematika, Tome 7 (1995) no. 3, pp. 8-18

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Let $\varkappa (T)$ be the height of a $q$-ary search tree $T$ constructed by the keys $K_1, K_2,\ldots,K_n$ each of which is a vector whose components belong to the alphabet $A=\{0,1,\ldots,q-1\}$. Assuming that the components of the vectors are independent and uniformly distributed on $A$, we find upper and lower estimates for the probabilities $\P\{\varkappa (t)\leq m\}$, $m=1,\ldots,n,$ with explicitly given constants. For typical values of $m $ the estimates obtained are better than those proved by Flajolet [2]. 
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     author = {V. A. Vatutin and V. G. Mikhailov},
     title = {Some estimates for the distribution of the height of a tree for digital searching},
     journal = {Diskretnaya Matematika},
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     publisher = {mathdoc},
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     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1995_7_3_a1/}
}
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V. A. Vatutin; V. G. Mikhailov. Some estimates for the distribution of the height of a tree for digital searching. Diskretnaya Matematika, Tome 7 (1995) no. 3, pp. 8-18. http://geodesic.mathdoc.fr/item/DM_1995_7_3_a1/