Cluster categories coming from cyclic posets

Cyclic poset are generalizations of cyclically ordered sets. In this paper we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The continuous cluster categories of arXiv:1209.1879 are examples of this construction. If we twist the construction using an admissible automorphism of the cyclic poset, we generate other examples such as the m-cluster category of type A-infinity (m>2).