Abstract
Stein's exchangeable perturbation technique is used to extend Yamamoto's Latin rectangle enumeration theorem to a class of rectangular arrays in which the proscription against matching within columns applies only to elements of a subset B of the set of positive integers. The allowable growth rate of the row-size of the array, as n → ∞, is determined by the growth rate of the number of elements in the set B ∩ {1, 2,…, n}, and the theorem holds so long as this latter rate exceeds n 1 2 .
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