  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.
