Abstract
This paper proves the conjectures (previously proved in the case n=0) that for any Coxeter system (W,S) and any natural number n, the set of n-small roots for W is bipodal and the set of n-low elements of W is a Garside shadow. The proof here uses special cases (k=3) of properties (notably, their existence) of certain maximal rank k reflection subgroups of W, for non-negative integers k.
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