Berenstein and Zelevinsky introduced quantum cluster algebras \cite{ BZ1} and the triangular bases \cite{ BZ2}. The support conjecture proposed in \cite{ LLRZ}, which asserts that the support of each triangular basis element for a rank-2 cluster algebra is bounded by an explicitly described region, was established in \cite{ L} for skew-symmetric rank-2 cluster algebras. In this paper we extend this result by proving a bound on the support of each triangular basis element for bipartite cluster algebras.
Categories: math.RT math.AG