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The dynamics of a one-sided subshift $\mathsf{X}$ can be modeled by a set ofpartially defined bijections. From this data we define an inverse semigroup$\mathcal{S}_{\mathsf{X}}$ and show that it has many interesting properties. Weprove that the Carlsen-Matsumoto C*-algebra $\mathcal{O}_\mathsf{X}$ associatedto $\mathsf{X}$ is canonically isomorphic to Exel's tight C*-algebra of$\mathcal{S}_{\mathsf{X}}$. As one consequence, we obtain that$\mathcal{O}_\mathsf{X}$ can be written as a partial crossed product of acommutative C*-algebra by a countable group.

Inverse semigroups associated to subshifts