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- W4312122020 abstract "It is proved that a multiset of permissible arcs over a tiling is uniquely determined by its intersection vector under a mild condition. This generalizes a classical result over marked surfaces with triangulations. We apply this result to study $tau$-tilting theory of gentle algebras and denominator conjecture in cluster algebras. In the case of gentle algebras, it is proved that different $tau$-rigid $A$-modules over a gentle algebra $A$ have different dimension vectors if and only if $A$ has no even oriented cycle with full relations. For cluster algebras, the denominator conjecture has been established for cluster algebras of type $mathbb{A}mathbb{B}mathbb{C}$." @default.
- W4312122020 created "2023-01-04" @default.
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- W4312122020 date "2022-12-22" @default.
- W4312122020 modified "2023-10-18" @default.
- W4312122020 title "Intersection vectors over tilings with applications to gentle algebras and cluster algebras" @default.
- W4312122020 doi "https://doi.org/10.48550/arxiv.2212.11497" @default.
- W4312122020 hasPublicationYear "2022" @default.
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