A conjecture on $C$-matrices of cluster algebras

Peigen Cao, Min Huang, Fang Li

For a skew-symmetrizable cluster algebra ${\mathcal{A}}_{t_0}$ with principal coefficients at $t_0$, we prove that each seed ${\Sigma }_t$ of ${\mathcal{A}}_{t_0}$ is uniquely determined by its…