TL;DR
This paper links friezes of type D-tilde with SL2-tilings of type A-tilde, enabling independent computation of all cluster variables in the associated cluster algebra.
Contribution
It establishes a novel relation between D-tilde friezes and A-tilde SL2-tilings, facilitating cluster variable calculations.
Findings
Derived explicit formulas for cluster variables.
Connected frieze patterns with SL2-tilings.
Enabled independent computation of cluster variables.
Abstract
In this article, we establish a relation between the values of a frieze of type D-tile and some values of an SL2-tiling t associated with a particular quiver of type A-tilde . This relation allows us to compute, independently of each other, all the cluster variables in the cluster algebra associated with a quiver Q of type D-tilde.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Topics in Algebra