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What is the name for an integer partition with bounded multiplicities?

For the first question, I called them "Andrews class partitions" in Limit Shapes via Bijections. For the second question, the complement condition $\mu_i - \mu_{i+1} \geq d$ is usually ...
Stephen DeSalvo's user avatar
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Asymptotics for number of $p$-regular partitions of $n$

This is answered in the paper of Peter Hagis, "Partitions with a restriction on the multiplicities of the summands" Trans AMS 155 (1971), 375-384. Corollary 4.2 at the end of the paper is ...
Dave Benson's user avatar
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