What question did this study set out to answer?

To develop an efficient algorithm for generating unlabeled Pólya trees, facilitating better statistical comparisons.

An algorithm for uniform generation of unlabeled (Pólya) trees

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Randomized algorithm generates unlabeled Pólya trees efficiently, suggesting better comparisons with labeled tree statistics.

To develop an efficient algorithm for generating unlabeled Pólya trees, facilitating better statistical comparisons.
Developed an algorithm utilizing the Burnside process for generating Pólya trees.
Alternated between creating a uniform permutation and producing labeled rooted trees.
Introduced a product formula refining Cayley's approach for counting permutations.
Demonstrated conjecturally efficient generation of Pólya trees.
Enabled comparison of statistics between unlabeled and labeled trees.
Provided a theoretical framework for asymptotic comparisons with practical data.

Bartholdi et al. (2026) studied this question.

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View Full Paper

Ask AI

Bookmark

Authors

Randomized algorithm generates unlabeled Pólya trees efficiently, suggesting better comparisons with labeled tree statistics.

To develop an efficient algorithm for generating unlabeled Pólya trees, facilitating better statistical comparisons.
Developed an algorithm utilizing the Burnside process for generating Pólya trees.
Alternated between creating a uniform permutation and producing labeled rooted trees.
Introduced a product formula refining Cayley's approach for counting permutations.
Demonstrated conjecturally efficient generation of Pólya trees.
Enabled comparison of statistics between unlabeled and labeled trees.
Provided a theoretical framework for asymptotic comparisons with practical data.

Bartholdi et al. (2026) studied this question.

View Full Paper

Ask AI

Bookmark