Conference proceeding
Partition polynomials: Asymptotics and zeros
TAPAS IN EXPERIMENTAL MATHEMATICS, Vol.457
CONTEMPORARY MATHEMATICS SERIES
01 Jan 2008
Abstract
Let F-n(x) be the partition polynomial Sigma(n)(k=1) 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 root 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.
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Details
- Title
- Partition polynomials: Asymptotics and zeros
- Creators
- Robert P. Boyer - Drexel UniversityWilliam M. Y. Goh - Drexel University
- Contributors
- T Amdebehan (Editor)V H Moll (Editor)
- Publication Details
- TAPAS IN EXPERIMENTAL MATHEMATICS, Vol.457
- Series
- CONTEMPORARY MATHEMATICS SERIES
- Publisher
- Amer Mathematical Soc
- Number of pages
- 13
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- [Retired Faculty]
- Identifiers
- 991019170561304721
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