Partition Polynomials: Asymptotics and Zeros

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dc.creatorBoyer, Robert P.
dc.creatorGoh, William M. Y.
dc.date2007-11-09
dc.date.accessioned2026-07-07T08:41:49Z
dc.date.available2026-07-07T08:41:49Z
dc.descriptionLet $F_n(x)$ be the partition polynomial $\sum_{k=1}^n p_k(n) x^k$ where $p_k(n)$ is the number of partitions of $n$ with $k$ parts. We emphasize the computational experiments using degrees up to $70,000$ to discover the asymptotics of these polynomials. Surprisingly, the asymptotics of $F_n(x)$ have two scales of orders $n$ and $\sqrt{n}$ and in three different regimes inside the unit disk. Consequently, the zeros converge to network of curves inside the unit disk given in terms of the dilogarithm.
dc.identifierhttps://arxiv.org/abs/0711.1373
dc.identifierhttp://arxiv.org/abs/0711.1373
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141796
dc.subjectCombinatorics
dc.subjectNumber Theory
dc.subject05C38, 15A15, 05A15, 15A18
dc.titlePartition Polynomials: Asymptotics and Zeros
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