Finite type and completeness of $g$-fans
Combinatorics
2025-12-29 v1
Abstract
We study the -fan associated with a skew-symmetrizable matrix in the sense of cluster algebras. We show that a skew-symmetrizable matrix is of finite type if and only if its -fan is complete; equivalently (as we show), its support contains all lattice points.
Cite
@article{arxiv.2512.21603,
title = {Finite type and completeness of $g$-fans},
author = {Toshiya Yurikusa},
journal= {arXiv preprint arXiv:2512.21603},
year = {2025}
}
Comments
5 pages