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The binary cumulant is defined for joint probability distributions on binary sequences of finite length. The binary cumulant is bounded, in magnitude, by unity, and is shown to vanish if there exists any bipartition of the letter positions into statistically independent blocks. Probability distributions on binary n-sequences are shown to map injectively into their binary cumulants for all subsets of the set of letter positions. An inversion algorithm is established, recovering the joint distribution from its collection of binary cumulants.
Document Type: Research Article
Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545