Birational Rowmotion and the Octahedron Recurrence
Combinatorics
2022-04-12 v1
Abstract
We use the octahedron recurrence to give a simplified statement and proof of a formula for iterated birational rowmotion on a product of two chains, first described by Musiker and Roby. Using this, we show that weights of certain chains in rectangles shift in a predictable way under the action of rowmotion. We then define generalized Stanley-Thomas words whose cyclic rotation uniquely determines birational rowmotion on the product of two chains. We also discuss the relationship between rowmotion and birational RSK and give a birational analogue of Greene's theorem in this setting.
Cite
@article{arxiv.2204.04255,
title = {Birational Rowmotion and the Octahedron Recurrence},
author = {Joseph Johnson and Ricky Ini Liu},
journal= {arXiv preprint arXiv:2204.04255},
year = {2022}
}