平面分区和在矩形和梯形上的移动

arXiv (Cornell University) Pub Date : 2023-11-13 DOI:10.48550/arxiv.2311.07133

Johnson, Joseph, Liu, Ricky Ini

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引用次数: 0

摘要

我们定义了一个矩形偏序集和它的关联的梯形偏序集的标记之间的双向映射。这张图热带化为这些固定高度的偏置集的平面分区之间的双射，给出了Proctor结果的一个新的双射证明。我们还证明了该映射对于两族运动是等变的，解决了Williams的一个猜想，并暗示了梯形偏集上的两族运动具有有限阶。

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Plane partitions and rowmotion on rectangular and trapezoidal posets

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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arXiv (Cornell University)

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