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We explore partitions that lie in the intersection of several sets ofclassical interest: partitions with parts indivisible by $m$, appearing fewerthan $m$ times, or differing by less than $m$. We find results on theirbehavior and generating functions: more results for those simultaneouslyregular and distinct, fewest for those distinct and flat. We offer someconjectures in the area.

Partitions into parts simultaneously regular, distinct, and/or flat