F-Matrices of Cluster Algebras from Triangulated Surfaces

For a given marked surface ( S ,  M ) and a fixed tagged triangulation T of ( S ,  M ), we show that each tagged triangulation T ′ of ( S ,  M ) is uniquely determined by the intersection numbers of tagged arcs of T and tagged arcs of T ′ . As a consequence, each cluster in the cluster algebra A ( T...

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Bibliographic Details
Published in:Annals of combinatorics 2020-12, Vol.24 (4), p.649-695
Main Authors: Gyoda, Yasuaki, Yurikusa, Toshiya
Format: Article
Language:English
Subjects:
Clusters
Combinatorics
Mathematics
Mathematics and Statistics
Triangulation
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Summary:For a given marked surface ( S ,  M ) and a fixed tagged triangulation T of ( S ,  M ), we show that each tagged triangulation T ′ of ( S ,  M ) is uniquely determined by the intersection numbers of tagged arcs of T and tagged arcs of T ′ . As a consequence, each cluster in the cluster algebra A ( T ) is uniquely determined by its F -matrix which is a new numerical invariant of the cluster introduced by Fujiwara and Gyoda.
ISSN:0218-0006
0219-3094
DOI:10.1007/s00026-020-00507-2