5 citations · 9 across the 9 of their papers we have counts for
10 papers
Lattice structure in cluster algebra of finite type and non-simply-laced Ingalls-Thomas bijection
Yasuaki Gyoda
In this paper, we demonstrate that the lattice structure of a set of clusters in a cluster algebra of finite type is anti-isomorphic to the torsion lattice of a certain Geiss-Lecle…
Generalization of Markov Diophantine equation via generalized cluster algebra
Yasuaki Gyoda, Kodai Matsushita
In this paper, we deal with two classes of Diophantine equations, and , where $k_1,…
Positive integer solutions to
Yasuaki Gyoda
In this paper, we give a specific way of describing positive integer solutions of a Diophantine equation and introduce a generalized cluster pattern…
Bongartz completion via -vectors
Peigen Cao, Yasuaki Gyoda, Toshiya Yurikusa
In the present paper, we first give a characterization for Bongartz completion in -tilting theory via -vectors. Motivated by this characterization, we give the definition of…
Positive cluster complexes and -tilting simplicial complexes of cluster-tilted algebras of finite type
Yasuaki Gyoda
In this study, we consider the positive cluster complex, a full subcomplex of a cluster complex the vertices of which are all non-initial cluster variables. In particular, we provi…
Cluster duality between Calkin-Wilf tree and Stern-Brocot tree
Yasuaki Gyoda
We find a duality between two well-known trees, the Calkin-Wilf tree and the Stern-Brocot tree, derived from cluster algebra theory. The vertex sets of these trees are the set of r…