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

Julien Leroy (1)

1 Mathematics Research Unit

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.

Mots clés: S-adic subshift; S-adic conjecture; Rauzy graph; factor complexity; special factor

Domaines: Mathématique discrète [cs.DM]

Julien Leroy. An S-adic characterization of minimal subshifts with first difference of complexity 1 ≤ p(n+1) - p(n) ≤ 2. Discrete Mathematics and Theoretical Computer Science, 2014, Vol. 16 no. 1 (1), pp.233-286. ⟨10.46298/dmtcs.1249⟩. ⟨hal-01179422⟩