Leap generators for supercritical composition schemes C = A ∘ B yield linear-time exact-size samplers whose output distribution on size-n objects has total variation distance (c + o(1)) n^{-1/2} from uniform.
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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.
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Leap generators for composition schemes
Leap generators for supercritical composition schemes C = A ∘ B yield linear-time exact-size samplers whose output distribution on size-n objects has total variation distance (c + o(1)) n^{-1/2} from uniform.
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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.