Toggleability Spaces of 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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.02493
- arXiv:
- arXiv:2406.02493
- Bibcode:
- 2024arXiv240602493M
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 27 pages, 4 figures, and 2 tables