The height of record‐biased trees

Given a permutation σ $$ \sigma , its corresponding binary search tree is obtained by recursively inserting the values ( 1 ) … n (1),\dots, (n) into so that label of each node larger than labels left subtree and smaller right subtree. In this article, we study height trees drawn from record-biased model permutations whose probability measure on set proportional to θ record {\theta}^{\mathrm{record}\left(\sigma \right)} where = | { i ∈ [ ] : ∀ j < > } \mathrm{record}\left(\sigma \right)=\mid \left\{i\in \left[n\right]:\forall j\sigma (j)\right\}\mid . We show built size with parameter \theta order + o ℙ max c ∗ log / \left(1+{o}_{\mathbb{P}}(1)\right)\max \left\{{c}^{\ast}\log n,\kern0.3em \log \left(1+n/\theta \right)\right\} hence extending previous results Devroye or random trees.