Title: Right Amenability And Growth Of Finitely Right Generated Left Group Sets,
Abstract: We introduce right generating sets, Cayley graphs, growth functions, types
and rates, and isoperimetric constants for left homogeneous spaces equipped
with coordinate systems; characterise right amenable finitely right generated
left homogeneous spaces with finite stabilisers as those whose isoperimetric
constant is $0$; and prove that finitely right generated left homogeneous
spaces with finite stabilisers of sub-exponential growth are right amenable, in
particular, quotient sets of groups of sub-exponential growth by finite
subgroups are right amenable.