{"paper":{"title":"An Algorithmic Approach to the Extensibility of Association Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Manuel Arora, Paul-Hermann Zieschang","submitted_at":"2012-09-27T18:05:30Z","abstract_excerpt":"An association scheme which is associated to a height t presuperscheme is said to be extensible to height t. Smith (1994, 2007) showed that an association scheme X=(Q,\\Gamma) of order d:=|Q| is Schurian iff X is extensible to height (d-2). In this work, we formalize the maximal height t_max(X) of an association scheme X as the largest positive integer such that X is extensible to height t (we also include the possibility t_max(X)=\\infty, which is equivalent to t_max(X)\\ge (d-2)). Intuitively, the maximal height provides a natural measure of how close an association scheme is to being Schurian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6312","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"}