On the Number of τ-Tilting Modules over Nakayama Algebras

Let Lambda(r)(n) be the path algebra of the linearly oriented quiver of type A with n vertices modulo the r-th power of the radical, and let (Lambda) over tilde (r)(n) be the path algebra of the cyclically oriented quiver of type (A) over tilde with n vertices modulo the r-th power of the radical. Adachi gave a recurrence relation for the number of tau-tilting modules over Lambda(r)(n). In this paper, we show that the same recurrence relation also holds for the number of tau-tilting modules over (Lambda) over tilde (r)(n). As an application, we give a new proof for a result by Asai on recurrence formulae for the number of support tau-tilting modules over Lambda(r)(n) and (Lambda) over tilde (r)(n).