Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Number of $\tau$-Tilting Modules over Nakayama Algebras   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 $\widetilde{\Lambda}^r_n$.

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The categories of this paper are: cs
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The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: eess