Séminaire Lotharingien de Combinatoire, 91B.58 (2024), 12 pp.
Joseph Johnson and Ricky Ini Liu
Plane Partitions and Rowmotion on Rectangular and Trapezoidal Posets
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.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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