The number of elements in the mutation class of a quiver of type \(D_n\). (Q1028827)
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| Language | Label | Description | Also known as |
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| English | The number of elements in the mutation class of a quiver of type \(D_n\). |
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The number of elements in the mutation class of a quiver of type \(D_n\). (English)
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8 July 2009
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Summary: We show that the number of quivers in the mutation class of a quiver of Dynkin type \(D_n\) is given by \(\sum_{d\mid n}\varphi(n/d)\binom{2d}{d}/(2n)\) for \(n\geq 5\). To obtain this formula, we give a correspondence between the quivers in the mutation class and certain rooted trees.
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cluster algebras
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Dynkin quivers
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mutations
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mutation classes
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