Equivalent combinatorial expansion formulas for generalized cluster algebras on punctured orbifolds are derived using snake graphs, labelled posets, matrices, and T-walks, generalizing prior results for surfaces and unpunctured orbifolds.
F-Polynomials of Donaldson-Thomas Transformations
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Using Hom-infinite Frobenius categorification of the Grassmannian, the authors determine g-vectors of Plücker coordinates for the triangular seed and express DT F-polynomials in terms of 3D Young diagrams, giving a new proof of Weng's theorem.
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Cluster Expansions from Punctured Orbifolds
Equivalent combinatorial expansion formulas for generalized cluster algebras on punctured orbifolds are derived using snake graphs, labelled posets, matrices, and T-walks, generalizing prior results for surfaces and unpunctured orbifolds.
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$g$-vectors and $DT$-$F$-polynomials for Grassmannians
Using Hom-infinite Frobenius categorification of the Grassmannian, the authors determine g-vectors of Plücker coordinates for the triangular seed and express DT F-polynomials in terms of 3D Young diagrams, giving a new proof of Weng's theorem.