  With each piecewise monotonic map of the unit interval, a dimension triple is
associated. The dimension triple, viewed as a Z[t, t^{-1}] module, is finitely
generated, and generators are identified. Dimension groups are computed for
Markov maps, unimodal maps, multimodal maps, and interval exchange maps. It is
shown that the dimension group defined here is isomorphic to K_0(A), where A is
a C*-algebra (an "AI-algebra") defined in dynamical terms.
