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Mathematics > Combinatorics
Title: Denseness of $g$-vector cones from weighted orbifolds
(Submitted on 5 Jul 2023 (v1), last revised 26 Apr 2024 (this version, v3))
Abstract: We study $g$-vector cones in a cluster algebra defined from a weighted orbifold of rank $n$ introduced by Felikson, Shapiro and Tumarkin. We determine the closure of the union of the $g$-vector cones. It is equal to $\mathbb{R}^n$ except for a weighted orbifold with empty boundary and exactly one puncture, in which case it is equal to the half space of a certain explicit hyperplane in $\mathbb{R}^n$.
Submission history
From: Toshiya Yurikusa [view email][v1] Wed, 5 Jul 2023 13:37:59 GMT (29kb)
[v2] Thu, 6 Jul 2023 04:32:43 GMT (29kb)
[v3] Fri, 26 Apr 2024 06:57:05 GMT (29kb)
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