On the dimension group of unimodular $${\mathcal {S}}$$-adic subshifts

Dimension groups are complete invariants of strong orbit equivalence for minimal Cantor systems. This paper studies a natural family systems having finitely generated dimension group, namely the primitive unimodular proper $${\mathcal {S}}$$ S -adic subshifts. They by iterating sequences substitutions. Proper substitutions such that images letters start with same letter, and similarly end letter. includes various classes subshifts as Brun or dendric subshifts, in turn include Arnoux–Rauzy coding interval exchange transformations. We compute their group investigate relation between triviality infinitesimal subgroup rational independence letter measures. also introduce notion balanced functions provide topological characterization balancedness S-adic