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.
arXiv preprint arXiv:2007.05483 , year=
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For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.
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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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Quantum cluster algebra realization for stated ${\rm SL}_n$-skein algebras and rotation-invariant bases for polygons
For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.