Newton polytopes in cluster algebras and $τ$-tilting theory
Abstract
We prove that the cluster monomials in non-initial cluster variables are uniquely determined by the Newton polytopes of their $F$-polynomials for skew-symmetrizable cluster algebras. Accordingly, we prove that the $τ$-rigid modules and the left finite multi-semibricks in $τ$-tilting theory are uniquely determined by the Newton polytopes of these modules. The key tools used in the proofs are the left Bongartz completion, $F$-invariant and partial $F$-invariant in the context of cluster algebras and $τ$-tilting theory.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Advanced Combinatorial Mathematics
Rings
Modules
and Algebras
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 8 February 2026
- Language
- EN
- Document type
- Preprint