{"paper":{"title":"Maximal spanning time for neighborhood growth on the Hamming plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erik Slivken, Janko Gravner, J.E. Paguyo","submitted_at":"2017-08-06T06:59:59Z","abstract_excerpt":"We consider a long-range growth dynamics on the two-dimensional integer lattice, initialized by a finite set of occupied points. Subsequently, a site $x$ becomes occupied if the pair consisting of the counts of occupied sites along the entire horizontal and vertical lines through $x$ lies outside a fixed Young diagram $\\mathcal{Z}$. We study the extremal quantity $\\mu(\\mathcal{Z})$, the maximal finite time at which the lattice is fully occupied. We give an upper bound on $\\mu(\\mathcal{Z})$ that is linear in the area of the bounding rectangle of $\\mathcal{Z}$, and a lower bound $\\sqrt{s-1}$, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01855","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"}