{"paper":{"title":"Multiple tilings associated to d-Bonacci beta-expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MG"],"primary_cat":"math.NT","authors_text":"Tom\\'a\\v{s} Hejda","submitted_at":"2015-03-24T23:36:13Z","abstract_excerpt":"Let $\\beta\\in(1,2)$ be a Pisot unit and consider the symmetric $\\beta$-expansions. We give a necessary and sufficient condition for the associated Rauzy fractals to form a tiling of the contractive hyperplane. For $\\beta$ a $d$-Bonacci number, i.e., Pisot root of $x^d-x^{d-1}-\\dots-x-1$ we show that the Rauzy fractals form a multiple tiling with covering degree $d-1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07744","kind":"arxiv","version":3},"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"}