On the Zeros of Plane Partition Polynomials - Boyer, Robert P.; Parry, Daniel T. (The Electronic Journal of Combinatorics, 2012)
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) = 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→∞. 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.