{"paper":{"title":"Central aspects of skew translation quadrangles, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Koen Thas","submitted_at":"2014-06-16T13:02:38Z","abstract_excerpt":"Except for the Hermitian buildings $\\mathcal{H}(4,q^2)$, up to a combination of duality, translation duality or Payne integration, every known finite building of type $\\mathbb{B}_2$ satisfies a set of general synthetic properties, usually put together in the term \"skew translation generalized quadrangle\" (STGQ). In this series of papers, we classify finite skew translation generalized quadrangles. In the first installment of the series, as corollaries of the machinery we develop in the present paper, (a) we obtain the surprising result that any skew translation quadrangle of odd order $(s,s)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4002","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"}