Geodesic
The number of elements in the mutation class of a quiver of type \(D_n\).
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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We show that the number of quivers in the mutation class of a quiver of Dynkin type $D_n$ is given by $\sum_{d|n}\phi(n/d){2d\choose d}/(2n)$ for $n \geq 5$. To obtain this formula, we give a correspondence between the quivers in the mutation class and certain rooted trees.
DOI : 10.37236/138
Classification : 16G20, 05A15
Mots-clés : cluster algebras, Dynkin quivers, mutations, mutation classes 
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     author = {Aslak Bakke Buan and Hermund Andr\'e Torkildsen},
     title = {The number of elements in the mutation class of a quiver of type {\(D_n\).}},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/138},
     zbl = {1175.16009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/138/}
}
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Aslak Bakke Buan; Hermund André Torkildsen. The number of elements in the mutation class of a quiver of type \(D_n\).. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/138

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