Frobenius–Perron dimension via tauτ τ -tilting theory

From the perspective of tau τ τ -tilting theory, we study Frobenius–Perron dimensions of finite-dimensional algebras. First, we evaluate the Frobenius–Perron dimensions of tau τ τ -tilting finite algebras by a combinatorial method in tau τ τ -tilting theory. Second, we give an upper bound for the Frobenius–Perron dimension of tau τ τ -tilting finite algebras of tame representation type. Third, we determine the Frobenius–Perron dimensions of Nakayama algebras and generalized preprojective algebras of Dynkin type in the sense of Geiß–Leclerc–Schröer.