Profiles of random trees: plane-oriented recursive trees

Abstract : We summarize several limit results for the profile of random plane-oriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximations of the expected width and the correlation coefficients of two level sizes. We also unveil an unexpected connection between the profile of plane-oriented recursive trees (with logarithmic height) and that of random binary trees (with height proportional to the square root of tree size).
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Conrado Martínez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.193-200, 2005, DMTCS Proceedings
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Hsien-Kuei Hwang. Profiles of random trees: plane-oriented recursive trees. Conrado Martínez. 2005 International Conference on Analysis of Algorithms, 2005, Barcelona, Spain. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms, pp.193-200, 2005, DMTCS Proceedings. 〈hal-01184033〉

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