Geodesic
Toggleability spaces of fences
Alec Mertin1 ; Svetlana Poznanović1
1Clemson University
The electronic journal of combinatorics, Tome 31 (2024) no. 4
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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.
DOI : 10.37236/13085
Classification : 05E18, 06A07
Mots-clés : fence poset, homomesy, homometry, rowmotion, tiling

Alec Mertin  1   ; Svetlana Poznanović  1

1 Clemson University 
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Alec Mertin; Svetlana Poznanović. Toggleability spaces of fences. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/13085

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