{"paper":{"title":"On the Hausdorff dimension faithfulness connected with $Q_{infty}$-expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jia Liu, Zhenliang Zhang","submitted_at":"2016-02-18T02:34:29Z","abstract_excerpt":"In this paper, we show that, the family of all possible union of finite consecutive cylinders of the same rank of $Q_{\\infty}$-expansion is faithful for the Hausdorff dimension calculation. Applying this result, we give the necessary and sufficient condition for the family of all cylinders of $Q_{\\infty}$-expansion to be faithful for Hausdorff dimension calculation on the unit interval, this answers the open problem mentioned in a paper of S. Albeverio et al.."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05662","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"}