  For each positive integer n, we define a polynomial in the variables
z_1,...,z_n with coefficients in the ring $\mathbb{Q}[q,t,r]$ of polynomial
functions of three parameters q, t, r. These polynomials naturally arise in the
context of cluster algebras. We conjecture that they are symmetric polynomials
in z_1,...,z_n, and that their expansions in terms of monomial, Schur, complete
homogeneous, elementary and power sum symmetric polynomials are sign-coherent.
