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On the Zeros of Plane Partition Polynomials
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 …