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arXiv · 2311.07133

Plane partitions and rowmotion on rectangular and trapezoidal posets

Joseph Johnson·Ricky Ini Liu
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Abstract

We define a birational map between labelings of a rectangular poset and its associated trapezoidal poset. This map tropicalizes to a bijection between the plane partitions of these posets of fixed height, giving a new bijective proof of a result by Proctor. We also show that this map is equivariant with respect to birational rowmotion, resolving a conjecture of Williams and implying that birational rowmotion on trapezoidal posets has finite order.

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Joseph Johnson, Ricky Ini Liu. 2023-11-13. Plane partitions and rowmotion on rectangular and trapezoidal posets. https://arxiv.org/abs/2311.07133

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