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arXiv · 2406.02493

Toggleability Spaces of Fences

Alec Mertin·Svetlana Poznanović
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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.

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Alec Mertin, Svetlana Poznanović. 2024-06-04. Toggleability Spaces of Fences. https://arxiv.org/abs/2406.02493

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