Skein relations for punctured surfaces
Skein relations for punctured surfaces
We investigate skein relations in cluster algebras from punctured surfaces, extending the work of \c{C}anak\c{c}i-Schiffler and Musiker-Williams on unpunctured surfaces. Using a combinatorial expansion formula by O\u{g}uz-Yildirim and Pilaud-Reading-Schroll, we provide explicit formulas for these relations. Our approach allows us to detail the $y$-monomials involved and identify that one term …