Sign changes in statistics for plane partitions

TL;DR

This paper investigates the asymptotic distribution of certain statistics in plane partitions and overpartitions, revealing secondary term behaviors and complex number controls through advanced analytical techniques.

Contribution

It introduces new asymptotic formulas for secondary terms in the distribution of plane partition statistics, extending analysis to related overpartition statistics.

Findings

Secondary terms are asymptotically characterized by complex numbers from twisted MacMahon products.

The trace of plane partitions exhibits equidistribution in residue classes mod b with detailed asymptotic behavior.

Analysis of related overpartition statistics shows similar asymptotic properties.

Abstract

Recent work of Cesana, Craig and the third author shows that the trace of plane partitions is asymptotically equidistributed in residue classes mod $b$. Applying a technique of the first two authors and Garnowski, we prove asymptotic formulas for the secondary terms in this equidistribution, which are controlled by certain complex numbers generated by a twisted MacMahon-type product. We further carry out a similar analysis for a statistic related to plane overpartitions.