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Discrete Mathematics & Theoretical Computer Science |
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.
Source : ScholeXplorer
HasVersion DOI 10.48550/arxiv.1812.05997
Regan, Samuel ; Slivken, Erik ; |