Geodesic
The number of occurrences of patterns in a random tree or forest permutation
Svante Janson1
1Uppsala University
The electronic journal of combinatorics, Tome 30 (2023) no. 2
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The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of these random permutations. The main results show that the distributions of these numbers are asymptotically normal. The proof uses representations of random tree and forest permutations that enable us to express the number of occurrences of a pattern by a type of U-statistics; we then use general limit theorems for the latter.
DOI : 10.37236/11111
Classification : 05C30, 05C80, 05C05, 60C05

Svante Janson  1

1 Uppsala University 
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Svante Janson. The number of occurrences of patterns in a random tree or forest permutation. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11111

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