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- W4300641741 abstract "A random binary search tree grown from the uniformly random permutation of $[n]$ is studied. We analyze the exact and asymptotic counts of vertices by rank, the distance from the set of leaves. The asymptotic fraction $c_k$ of vertices of a fixed rank $kge 0$ is shown to decay exponentially with $k$. Notoriously hard to compute, the exact fractions $c_k$ had been determined for $kle 3$ only. We computed $c_4$ and $c_5$ as well; both are ratios of enormous integers, denominator of $c_5$ being $274$ digits long. Prompted by the data, we proved that, in sharp contrast, the largest prime divisor of $c_k$'s denominator is $2^{k+1}+1$ at most. We conjecture that, in fact, the prime divisors of every denominator for $k>1$ form a single interval, from $2$ to the largest prime not exceeding $2^{k+1}+1$." @default.
- W4300641741 created "2022-10-03" @default.
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- W4300641741 date "2014-12-08" @default.
- W4300641741 modified "2023-09-26" @default.
- W4300641741 title "On a random search tree: asymptotic enumeration of vertices by distance from leaves" @default.
- W4300641741 doi "https://doi.org/10.48550/arxiv.1412.2796" @default.
- W4300641741 hasPublicationYear "2014" @default.
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