On the zeros of plane partition polynomials
The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2
Let $PL(n)$ be the number of all plane partitions of $n$ while $pp_k(n)$ be the number of plane partitions of $n$ whose trace is exactly $k$. We study the zeros of polynomial versions $Q_n(x)$ of plane partitions where $Q_n(x) = \sum pp_k(n) x^k$. Based on the asymptotics we have developed for $Q_n(x)$ and computational evidence, we determine the limiting behavior of the zeros of $Q_n(x)$ as $n\to\infty$. The distribution of the zeros has a two-scale behavior which has order $n^{2/3}$ inside the unit disk while has order $n$ on the unit circle.
DOI :
10.37236/2026
Classification :
11C08, 05A15, 05A16, 11M35, 30C15
Mots-clés : asymptotic, phase, plane partition, polylogarithm
Mots-clés : asymptotic, phase, plane partition, polylogarithm
@article{10_37236_2026,
author = {Robert P. Boyer and Daniel T. Parry},
title = {On the zeros of plane partition polynomials},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {2},
doi = {10.37236/2026},
zbl = {1243.11020},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2026/}
}
Robert P. Boyer; Daniel T. Parry. On the zeros of plane partition polynomials. The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2. doi: 10.37236/2026
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