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arXiv · 1812.05997

Expected size of a tree in the fixed point forest

Samuel Regan·Erik Slivken
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Abstract

We study the local limit of the fixed-point forest, a tree structure associated to a simple sorting algorithm on permutations. This local limit can be viewed as an infinite random tree that can be constructed from a Poisson point process configuration on $[0,1]^\mathbb{N}$. We generalize this random tree, and compute the expected size and expected number of leaves of a random rooted subtree in the generalized version. We also obtain bounds on the variance of the size.

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Samuel Regan, Erik Slivken. 2018-12-14. Expected size of a tree in the fixed point forest. https://doi.org/10.23638/dmtcs-21-2-1

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