An S-adic characterization of minimal subshifts with first difference of complexity 1 ≤ p(n+1) - p(n) ≤ 2

Abstract : An S-adic characterization of minimal subshifts with first difference of complexity 1 ≤ p(n + 1) − p(n) ≤ 2 S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is S-adic with Card(S) ≤ 3 27. In this paper, we improve this result by giving an S-adic characterization of these subshifts with a set S of 5 morphisms, solving by this way the S-adic conjecture for this particular case.