English

Finite type and completeness of $g$-fans

Combinatorics 2025-12-29 v1

Abstract

We study the gg-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 gg-fan is complete; equivalently (as we show), its support contains all lattice points.

Keywords

Cite

@article{arxiv.2512.21603,
  title  = {Finite type and completeness of $g$-fans},
  author = {Toshiya Yurikusa},
  journal= {arXiv preprint arXiv:2512.21603},
  year   = {2025}
}

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5 pages