Lattice paths and generalized cluster complexes

In this paper we propose a variant of the generalized Schrِder paths and generalized Delannoy paths by giving a restriction on the positions of certain steps. This generalization turns out to be reasonable, as attested by the connection with the faces of generalized cluster complexes of types A and B. As a result, we derive Krattenthalerʹs F-triangles for these two types by a combinatorial approach in terms of lattice paths.