{"paper":{"title":"On $K_0$-Groups for Substitution Tilings","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"cond-mat","authors_text":"Johannes Kellendonk","submitted_at":"1995-03-02T16:27:03Z","abstract_excerpt":"The group $C(\\Om,\\Z)/\\E$ is determined for tilings which are invariant under a locally invertible primitive \\sst\\ which forces its \\saum. In case the tiling may be obtained by the generalized dual method from a regular grid this group furnishes part of the $K_0$-group of the algebra of the tiling. Applied to Penrose tilings one obtains $K_0(\\A_\\tl)=\\Z^8\\oplus\\Z$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9503017","kind":"arxiv","version":2},"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"}