Toggleability Spaces of Fences
Alec Mertin, Svetlana Poznanovi\'c
TL;DR
This paper characterizes toggleability spaces for fences, enabling the strengthening of known homomesy results and establishing new ones across various rowmotion settings in combinatorics.
Contribution
It provides a complete description of toggleability spaces for fences, advancing understanding of homomesy phenomena in combinatorial dynamics.
Findings
Strengthens existing homomesy results under rowmotion.
Proves new homomesy results for combinatorial, piecewise-linear, and birational rowmotion.
Describes the structure of toggleability spaces for general fences.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Commutative Algebra and Its Applications · Polynomial and algebraic computation