Let T be a k-linear Hom-finite (n+ 2)-angulated category with n-suspension functor Sigma(n), split idempotents, and Serre functor S. Let T be an Oppermann-Thomas cluster tilting object in T with endomorphism algebra Gamma = End(T) (T). We introduce the notions of relative Oppermann-Thomas cluster tilting objects and support tau(n)-tilting pairs, and show that there is an bijection between the set of isomorphism classes of basic relative Oppermann-Thomas cluster tilting objects in T and the set of isomorphism classes of basic support tau(n)-tilting pairs in an n-cluster tilting subcategory of mod Gamma. As applications, we recover the Yang-Zhu bijection (Trans Am Math Soc 371:387-412, 2019) and Adachi-Iyama-Reiten bijection (Compos Math 150:415-452, 2014), and we give a natural partial order for relative Oppermann-Thomas cluster tilting objects.
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