{"paper":{"title":"Substitutions, tiling dynamical systems and minimal self-joinings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Younghwan Son","submitted_at":"2014-02-23T20:55:28Z","abstract_excerpt":"We investigate substitution subshifts and tiling dynamical systems arising from the substitutions (1) \\theta : 0 \\rightarrow 001,1 \\rightarrow 11001 and (2) \\eta : 0 \\rightarrow 001,1 \\rightarrow 11100. We show that the substitution subshifts arising from \\theta and \\eta have minimal self-joinings and are mildly mixing. We also give a criterion for 1-dimensional tiling systems arising from \\theta or \\eta to have minimal self-joinings. We apply this to obtain examples of mildly mixing 1-dimensional tiling systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5672","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"}