On the number of $\tau $-tilting modules over the Auslander algebras of radical square zero Nakayama algebras

Let Λ n be a radical square zero Nakayama algebra with n simple modules and Γ n the Auslander algebra of Λ n . We calculate the number j τ - tilt Γ n j of τ -tilting modules and the number j s τ - tilt Γ n j of support τ -tilting modules over Γ n . In particular, we prove that there are recurrence relations: from which the exact values of j τ - tilt Γ n j and j s τ - tilt Γ n j are derived. Mathematics