{"paper":{"title":"The computation of overlap coincidence in Taylor-Socolar substitution tiling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.MG","authors_text":"Jeong-Yup Lee, Shigeki Akiyama","submitted_at":"2012-12-18T01:33:58Z","abstract_excerpt":"Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tiling can be viewed as a substitution tiling. We use the substitution rule for this tiling and apply the algorithm of \\cite{AL} to check overlap coincidence. It turns out that the tiling has overlap coincidence. So the tiling dynamics has pure point spectrum and we can conclude that this tiling has a quasicrystalline structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4209","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"}