Plane partitions and rowmotion on rectangular and trapezoidal posets
Combinatorics
2023-11-14 v1
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.
Cite
@article{arxiv.2311.07133,
title = {Plane partitions and rowmotion on rectangular and trapezoidal posets},
author = {Joseph Johnson and Ricky Ini Liu},
journal= {arXiv preprint arXiv:2311.07133},
year = {2023}
}
Comments
40 pages, 17 figures