Partition Polynomials: Asymptotics and Zeros

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Let Fₙ(x) be the partition polynomial ∑ₖ₌₁ⁿ pₖ(n) xᵏ where pₖ(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 Fₙ(x) have two scales of orders n and √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.