Parametrizing recollement data for triangulated categories

We give a general parametrization of all the recollement data for a triangulated category with a set of generators. From this we deduce a characterization of when a ℵ0-perfectly generated (or aisled) triangulated category is a recollement of triangulated categories generated by a single compact object. Also, we use homological epimorphisms to give a complete and explicit description of all the recollement data for (or smashing subcategories of) the derived category of a k-flat dg category. In the final part we give a bijection between smashing subcategories of compactly generated triangulated categories and certain ideals of the subcategory of compact objects, in the spirit of H. Krause's work [Henning Krause, Cohomological quotients and smashing localizations, Amer. J. Math. 127 (2005) 1191–1246]. This bijection implies the following weak version of the generalized smashing conjecture: in a compactly generated triangulated category every smashing subcategory is generated by a set of Milnor colimits of compact objects.