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arXiv · 2205.11982

Holonomic equations and efficient random generation of binary trees

Pierre Lescanne
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Abstract

Holonomic equations are recursive equations which allow computing efficiently numbers of combinatoric objects. R{é}my showed that the holonomic equation associated with binary trees yields an efficient linear random generator of binary trees. I extend this paradigm to Motzkin trees and Schr{ö}der trees and show that despite slight differences my algorithm that generates random Schr{ö}der trees has linear expected complexity and my algorithm that generates Motzkin trees is in O(n) expected complexity, only if we can implement a specific oracle with a O(1) complexity. For Motzkin trees, I propose a solution which works well for realistic values (up to size ten millions) and yields an efficient algorithm.

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Pierre Lescanne. 2024-01-23. Holonomic equations and efficient random generation of binary trees. https://arxiv.org/abs/2205.11982

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