Toggleability Spaces of Fences
Combinatorics
2024-06-05 v1
Abstract
We completely describe the order ideal (resp. antichain) toggleability space for general fences: the space of statistics which are linear combinations of order ideal (antichain) indicator functions and equal to a constant plus a linear combination of toggleability statistics. This allows us to strengthen some homomesies under rowmotion on fences proven by Elizalde et al. and prove some new homomesy results for combinatorial, piecewise-linear, and birational rowmotion.
Keywords
Cite
@article{arxiv.2406.02493,
title = {Toggleability Spaces of Fences},
author = {Alec Mertin and Svetlana Poznanović},
journal= {arXiv preprint arXiv:2406.02493},
year = {2024}
}
Comments
27 pages, 4 figures, and 2 tables