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Formulas for the number of the augmented-data-manipulator (ADM)-passable permutations were given previously as cross-recurrence relations for the cardinalities of three specific subsets of such permutations. More concise, transparent recurrence formulas are derived utilizing a novel and conceptually simple model of the ADM. As a byproduct, a global control algorithm for the inverse ADM (IADM) i
omega passable permutations; ADM-passable permutations; augmented data manipulator network; cross-recurrence relations; transparent recurrence formulas; global control algorithm; inverse ADM; IADM-passable permutations; local control algorithms; signed bit difference tag control; destination tag control; multiprocessor interconnection networks; parallel processing.

D. Lee and K. Lee, "On the Augmented Data Manipulator Network in SIMD Environments," in IEEE Transactions on Computers, vol. 37, no. , pp. 574-584, 1988.
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