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Research in Number Theory. 7
Let $$\varDelta _d^{(a,b)}(n) = q_d^{(a)}(n) - Q_d^{(b)}(n)$$ where $$q_d^{(a)}(n)$$ counts the number of partitions of n into parts with difference at least d and size at least a, and $$Q_d^{(b)}(n)$$ counts the number of partitions into parts $$\eq