The ideal of relations for two generating sets of skein algebras S_n of the n-holed disk is generated by bounded-degree relations supported on subsurfaces with at most 6 holes (when q+q^{-1} invertible) or n holes (otherwise).
Santharoubane, Algebraic generators of the skein algebra of a surface
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On skein algebras of planar surfaces
The ideal of relations for two generating sets of skein algebras S_n of the n-holed disk is generated by bounded-degree relations supported on subsurfaces with at most 6 holes (when q+q^{-1} invertible) or n holes (otherwise).