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On equidistribution theorem for plane partitions
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DOI：10.1016/j.ejc.2026.104394.png)
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Abstract
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We prove equidistribution of two pairs of statistics on boxed plane partitions: (volume, trace) and (corner-hook volume, number of corners). The proof relies on different 3d visualizations of the corresponding non-intersecting path systems. In particular, we obtain a new visual proof for a volume generating function of plane partitions. We also introduce a new statistic called the cohook area on ordinary partitions, and prove that it is equidistributed with the area of partitions. (c) 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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