Cluster algebras arising from cluster tubes I: integer vectors

We study cluster algebras arising from cluster tubes. We obtain categorical interpretations for g -vectors, c -vectors and denominator vectors for cluster algebras of type C with respect to arbitrary initial seeds. In particular, a denominator theorem has been proved, which enables us to establish the linearly independence of denominator vectors of cluster variables from the same cluster for cluster algebras of type A B C . This strengthens the link between cluster tubes and cluster algebras of type C initiated by Buan, Marsh and Vatne.