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

对于最小的Cantor系统，维组是强轨道等价的完全不变量。本文研究了具有有限生成维组的最小Cantor系统的自然族，即原始单模固有\（{\ mathcal {S}} \\-adic子转换。它们是通过迭代替换序列生成的。适当的替换使得字母的图像以相同的字母开头，并且类似地以相同的字母结尾。这个家族包括各种子移位，例如Br​​un子移位或dendric子移位，而这些子移位又包括Arnoux-Rauzy子移位和间隔交换转换的自然编码。我们计算它们的维数组，并研究无穷小子组的琐碎性与字母度量的有理独立性之间的关系。我们还介绍了平衡函数的概念，并为原始单模态适当的S-adic子移位提供了平衡性的拓扑特征。