Counting the number of group orbits by marrying the Burnside process with importance sampling

Persi Diaconis; Chenyang Zhong

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arXiv · 2501.11731

Counting the number of group orbits by marrying the Burnside process with importance sampling

Persi Diaconis·Chenyang Zhong

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Abstract

This paper introduces a novel and general algorithm for approximately counting the number of orbits under group actions. The method is based on combining the Burnside process and importance sampling. Specializing to unitriangular groups yields an efficient algorithm for estimating the number of conjugacy classes of such groups.

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BibTeX RIS

Persi Diaconis, Chenyang Zhong. 2025-01-20. Counting the number of group orbits by marrying the Burnside process with importance sampling. https://arxiv.org/abs/2501.11731

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