Counting the number of group orbits by marrying the Burnside process with importance sampling
Probability
2025-03-21 v2 Combinatorics
Group Theory
Computation
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.
Keywords
Cite
@article{arxiv.2501.11731,
title = {Counting the number of group orbits by marrying the Burnside process with importance sampling},
author = {Persi Diaconis and Chenyang Zhong},
journal= {arXiv preprint arXiv:2501.11731},
year = {2025}
}
Comments
23 pages, 6 figures