Geodesic
Around the root of random multidimensional quadtrees
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006).

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We analyse the distribution of the root pattern of randomly grown multidimensional point quadtrees. In particular, exact, recursive and asymptotic formulas are given for the expected arity of the root. 
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     author = {Labelle, Gilbert and Laforest, Louise and Proven\c{c}al, Xavier},
     title = {Around the root of random multidimensional quadtrees},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities},
     year = {2006},
     doi = {10.46298/dmtcs.3484},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3484/}
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Labelle, Gilbert; Laforest, Louise; Provençal, Xavier. Around the root of random multidimensional quadtrees. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006). doi : 10.46298/dmtcs.3484. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3484/

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