Geodesic
On the Number of $\tau$-Tilting Modules over Nakayama Algebras
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\Lambda^r_n$ be the path algebra of the linearly oriented quiver of type $\mathbb{A}$ with $n$ vertices modulo the $r$-th power of the radical, and let $\widetilde{\Lambda}^r_n$ be the path algebra of the cyclically oriented quiver of type $\widetilde{\mathbb{A}}$ 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 $\widetilde{\Lambda}^r_n$. 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 $\widetilde{\Lambda}^r_n$.
Keywords: $\tau$-tilting modules, support $\tau$-tilting modules, Nakayama algebras. 
@article{SIGMA_2020_16_a57,
     author = {Hanpeng Gao and Ralf Schiffler},
     title = {On the {Number} of $\tau${-Tilting} {Modules} over {Nakayama} {Algebras}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a57/}
}
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Hanpeng Gao; Ralf Schiffler. On the Number of $\tau$-Tilting Modules over Nakayama Algebras. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a57/

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