An interactive implementation of the sampling algorithm in "Markov chains on Weyl groups from the geometry of the flag variety." Adjust the field characteristic and starting element. By the results of our paper, choosing a large characteristic gives Steinberg cell clusters, while a small one gives near-uniform randomness!
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Permutation-State Histogram
Lexicographic order on S_n; same color means same right Steinberg cell, via the RSK insertion tableau P