Duality between FinalSeed and InitialSeed Mutations in Cluster Algebras
Abstract
We study the duality between the mutations and the initialseed mutations in cluster algebras, where the initialseed mutations are the transformations of rational expressions of cluster variables in terms of the initial cluster under the change of the initial cluster. In particular, we define the maximal degree matrices of the $F$polynomials called the $F$matrices and show that the $F$matrices have the selfduality which is analogous to the duality between the $C$ and $G$matrices.
 Publication:

SIGMA
 Pub Date:
 May 2019
 DOI:
 10.3842/SIGMA.2019.040
 arXiv:
 arXiv:1808.02156
 Bibcode:
 2019SIGMA..15..040F
 Keywords:

 cluster algebra; mutation; duality;
 Mathematics  Rings and Algebras;
 Mathematics  Combinatorics;
 Mathematics  Representation Theory;
 13F60
 EPrint:
 SIGMA 15 (2019), 040, 24 pages