On the growth of restricted integer partition functions - Mathematics > CombinatoricsReport as inadecuate




On the growth of restricted integer partition functions - Mathematics > Combinatorics - Download this document for free, or read online. Document in PDF available to download.

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 $n$?



Author: E. Rodney Canfield, Herbert S. Wilf

Source: https://arxiv.org/







Related documents