{"paper":{"title":"On the geometry of the countably branching diamond graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.FA"],"primary_cat":"math.MG","authors_text":"Denka Kutzarova, Florent P. Baudier, Nirina L. Randrianarivony, Ryan Causey, Sheng Zhang, Stephen DIlworth, Thomas Schlumprecht","submitted_at":"2016-12-06T20:37:59Z","abstract_excerpt":"In this article, the bi-Lipschitz embeddability of the sequence of countably branching diamond graphs $(D_k^\\omega)_{k\\in\\mathbb{N}}$ is investigated. In particular it is shown that for every $\\varepsilon>0$ and $k\\in\\mathbb{N}$, $D_k^\\omega$ embeds bi-Lipschiztly with distortion at most $6(1+\\varepsilon)$ into any reflexive Banach space with an unconditional asymptotic structure that does not admit an equivalent asymptotically uniformly convex norm. On the other hand it is shown that the sequence $(D_k^\\omega)_{k\\in\\mathbb{N}}$ does not admit an equi-bi-Lipschitz embedding into any Banach spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01984","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"}