Plane partition polynomial asymptotics

Asymptotics for Rank Partition Functions

In this paper, we obtain asymptotic formulas for an infinite class of rank generating functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.

Partition Polynomials: Asymptotics and Zeros

Let Fn(x) be the partition polynomial ∑k=1 pk(n)x 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 netw...

Asymptotics of several-partition Hurwitz numbers

We derive in this paper the asymptotics of several-partition Hurwitz numbers, relying on a theorem of Kazarian for the one-partition case and on an induction carried on by Zvonkine. Essentially, the asymptotics for several partitions is the same as the one-partition asymptotics obtained by concatenating the partitions. Résumé. Dans cet article, nous donnons l’asymptotique générale des nombres d...

Determinants in Plane Partition Enumeration

In this paper we provide a new and concise evaluation of det ij + x + i + j j 05i;j5n?1 : This determinant arose in the enumeration of certain set of plane partitions. Its previous evaluation was lengthy and complicated.

Partition Analysis Xii: Plane Partitions