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Abstract: We study the rate of growth of $pn,S,M$, the number of partitions of $n$whose parts all belong to $S$ and whose multiplicities all belong to $M$, where$S$ resp. $M$ are given infinite sets of positive resp. nonnegativeintegers. We show that if $M$ is all nonnegative integers then $pn,S,M$cannot be of only polynomial growth, and that no sharper statement can be made.We ask: if $pn,S,M>0$ for all large enough $n$, can $pn,S,M$ be ofpolynomial growth in $n$?



Autor: E. Rodney Canfield, Herbert S. Wilf

Fuente: https://arxiv.org/







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