Plane partitions and rowmotion on rectangular and trapezoidal posets

Joseph Johnson; Ricky Ini Liu

Plane partitions and rowmotion on rectangular and trapezoidal posets

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arxiv 2311.07133 v1 pith:SM3556S4 submitted 2023-11-13 math.CO

Joseph Johnson , Ricky Ini Liu This is my paper · ORCID

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keywords birationalposetsrowmotiontrapezoidalpartitionsplaneposetrectangular

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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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Cyclic Sieving for Staircase Plane Partitions via Crystals and Electrical Networks
math.CO 2026-07 conditional novelty 4.0 of 10

Height-two staircase plane partitions satisfy cyclic sieving for promotion, proved by mapping promotion to rotation of 3-noncrossing perfect matchings via crystals and the electrical-network bush basis.

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