A conjecture on $C$-matrices of cluster algebras

Peigen Cao, Min Huang, Fang Li

Published 2017-02-04Version 1

In skew-symmetrizable case, we give a positive affirmation to a conjecture proposed by Sergey Fomin and Andrei Zelevinsky, which says each seed $\Sigma_t$ is uniquely determined by its {\bf C-matrix} in a cluster algebra $\mathcal A(\Sigma_{t_0})$ with principle coefficients at $t_0$. More discussion is given in the sign-skew-symmetric case so as to obtain a conclusion as weak version of the conjecture in this general case.