{"paper":{"title":"Embedding of self-similar ultrametric Cantor sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"A. Julien, J. Savinien","submitted_at":"2010-08-02T09:35:40Z","abstract_excerpt":"We study self-similar ultrametric Cantor sets arising from stationary Bratteli diagrams. We prove that such a Cantor set C is bi-Lipschitz embeddable in R^(d+1), where d denotes the integer part of its Hausdorff dimension. We compute this Hausdorff dimension explicitly and show that it is the abscissa of convergence of a zeta-function associated with a natural nerve of coverings of C (given by the Bratteli diagram). As a corollary we prove that the transversal of a (primitive) substitution tiling of R^d is bi-Lipschitz embeddable in R^(d+1) . We also show that C is bi-Hoelder embeddable in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0264","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"}