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- W792334787 abstract "We present an initial-seed-mutation formula for d-vectors of cluster variables in a cluster algebra. We also give two rephrasings of this recursion: one as a duality formula for d-vectors in the style of the g-vectors/c-vectors dualities of Nakanishi and Zelevinsky, and one as a formula expressing the highest powers in the Laurent expansion of a cluster variable in terms of the d-vectors of any cluster containing it. We prove that the initial-seed-mutation recursion holds in a varied collection of cluster algebras, but not in general. We conjecture further that the formula holds for source-sink moves on the initial seed in an arbitrary cluster algebra, and we prove this conjecture in the case of surfaces." @default.
- W792334787 created "2016-06-24" @default.
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- W792334787 date "2018-01-01" @default.
- W792334787 modified "2023-10-16" @default.
- W792334787 title "Initial-seed recursions and dualities for d-vectors" @default.
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- W792334787 doi "https://doi.org/10.2140/pjm.2018.293.179" @default.
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