{"paper":{"title":"An $S$-adic characterization of minimal subshifts with first difference of complexity $1 \\leq p(n+1) - p(n) \\leq 2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Julien Leroy","submitted_at":"2013-05-02T13:53:28Z","abstract_excerpt":"In [Ergodic Theory Dynam. System, 16 (1996) 663--682], S. Ferenczi proved that any minimal subshift with first difference of complexity bounded by 2 is $S$-adic with $\\card S \\leq 3^{27}$. In this paper, we improve this result by giving an $S$-adic charaterization of these subshifts with a set $S$ of 5 morphisms, solving by this way the $S$-adic conjecture for this particular case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0434","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}