Positivity in coefficient-free rank two cluster algebras

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dc.creatorDupont, G.
dc.date2009-03-15
dc.date.accessioned2026-07-07T12:52:48Z
dc.date.available2026-07-07T12:52:48Z
dc.descriptionLet $b,c$ be positive integers, $x_1,x_2$ be indeterminates over $\Z$ and $x_m, m \in \mathbb Z$ be rational functions defined by $x_{m-1}x_{m+1}=x_m^b+1$ if $m$ is odd and $x_{m-1}x_{m+1}=x_m^c+1$ if $m$ is even. In this short note, we prove that for any $m,k \in \Z$, $x_k$ can be expressed as a substraction-free Laurent polynomial in $\Z[x_m^{\pm 1},x_{m+1}^{\pm 1}]$. This proves Fomin-Zelevinsky's positivity conjecture for coefficient-free rank two cluster algebras.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/0903.2677
dc.identifierhttp://arxiv.org/abs/0903.2677
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223416
dc.subjectRings and Algebras
dc.subjectRepresentation Theory
dc.subject16S99; 16G20; 05E99
dc.titlePositivity in coefficient-free rank two cluster algebras
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