Séminaire Lotharingien de Combinatoire, 91B.81 (2024), 12 pp.
Esther Banaian, Wonwoo Kang and Elizabeth Kelley
Skein Relations for Punctured Surfaces
Abstract.
We use a combinatorial expansion formula for cluster algebras of surface type via order ideals of posets to give explicit skein relations for elements of a cluster algebra arising from a punctured surfaces. An immediate corollary of this is that the bangles and bracelets of Musiker, Schiffler, and Williams, which are known to provide a basis in the unpunctured case, form a spanning set in the punctured case.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
The following versions are available: