Toggleability Spaces of Fences

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 stren...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 31; no. 4
Main Authors Mertin, Alec, Poznanović, Svetlana
Format Journal Article
LanguageEnglish
Published 29.11.2024
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Summary: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.
ISSN:1077-8926
1077-8926
DOI:10.37236/13085