2023/11/13 by Joseph Johnson, Johnson, Joseph, Ricky Ini Liu +1
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2311.07133
openalex publication_date 2023/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.