English

On equidistribution theorem for plane partitions

Combinatorics 2026-05-15 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2605.14706,
  title  = {On equidistribution theorem for plane partitions},
  author = {Alimzhan Amanov and Damir Yeliussizov},
  journal= {arXiv preprint arXiv:2605.14706},
  year   = {2026}
}