Abstract
Functions defined over a 2 by k integer lattice that have a particular decomposition in terms of partitions over that lattice can be decomposed into disjoint classes, where each class can be generated by a transitive group action. Coset representatives can be shown to form a one to one correspondence with each disjoint class. As a consequence, this approach provides a way of algebraically enumerating the functions in question and is used in obtaining the asymptotic variance of an estimator of the fourth order cumulant spectral density.
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