The sign-coherence conjecture for denominator vectors
The sign-coherence conjecture for denominator vectors
Let be the denominator vectors of the cluster variables at a vertex relative to the initial vertex . A collection of vectors is sign-coherent if, in each coordinate, all vectors have either nonnegative or nonpositive entries. Sign-coherence conjecture for denominator vectors. For every and , the vectors are sign-coherent. The paper notes that this follows from the preceding denominator-vector conjecture and proves it on the bipartite belt; it remains open in general.
Sources & referencesView supporting material
Primary source
Sergey Fomin and Andrei Zelevinsky, “Cluster algebras IV: Coefficients”, arXiv:math/0602259 (2006).
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