Introduces the dual Burnside process via role interchange, proves it shares all nonzero eigenvalues with the classical kernel through matrix factorization, and demonstrates orbit and conjugacy lumpings plus fixed-symbol quotients that reduce state space while preserving spectrum.
Diaconis,Group Representations in Probability and Statistics, IMS Lecture Notes—Monograph 11, 1988
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The dual Burnside process
Introduces the dual Burnside process via role interchange, proves it shares all nonzero eigenvalues with the classical kernel through matrix factorization, and demonstrates orbit and conjugacy lumpings plus fixed-symbol quotients that reduce state space while preserving spectrum.