Distributive lattices and the poset of pre-projective tilting modules

D.Happel and L.Unger defined a partial order on the set of basic tilting modules. We study the poset of basic pre-projective tilting modules over path algebra of infinite type. We give an equivalent condition for that this poset is a distributive lattice. We also give an equivalent condition for that a distributive lattice is isomorphic to the poset of basic pre-projective tilting modules over a path algebra of representation infinite type.