On the Number of $\tau $-Tilting Modules over the Auslander Algebras of Radical Square Zero Nakayama Algebras

Let Lambda(n) be a radical square zero Nakayama algebra with n simple modules and the Auslander algebra of Lambda(n). We calculate the number |tau -tilt Gamma(n)| of tau-tilting modules and the number |s tau -tilt Gamma(n)| of support tau -tilting modules over Gamma(n) In particular, we prove the recurrence relations |tau -tilt Gamma(n)| = 3|tau -tilt Gamma(n) + |tau -tilt Gamma(n-2)| |s tau -tilt Gamma(n)| = 6|s tau -tilt Gamma(n-1)| + 3|s tau -tilt Gamma(n-2)| from which the exact values of |tau -tilt Gamma(n)| and |s tau -tilt Gamma(n)| are derived.