On equidistribution theorem for plane partitions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913128919334912 |
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| author | Amanov, Alimzhan Yeliussizov, Damir |
| author_facet | Amanov, Alimzhan Yeliussizov, Damir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14706 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On equidistribution theorem for plane partitions Amanov, Alimzhan Yeliussizov, Damir Combinatorics 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. |
| title | On equidistribution theorem for plane partitions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.14706 |