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arXiv · 2207.14590

Sign changes in statistics for plane partitions

Walter Bridges·Johann Franke·Joshua Males
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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.

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Walter Bridges, Johann Franke, Joshua Males. 2022-07-29. Sign changes in statistics for plane partitions. https://arxiv.org/abs/2207.14590

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