{"paper":{"title":"Catalan States of Lattice Crossing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Changsong Li, Jozef H. Przytycki, Mieczyslaw K. Dabkowski","submitted_at":"2014-09-14T15:25:43Z","abstract_excerpt":"For a Lattice crossing $L\\left( m,n\\right) $ we show which Catalan connection between $2\\left( m+n\\right) $ points on boundary of $m\\times n$ rectangle $P$ can be realized as a Kauffman state and we give an explicit formula for the number of such Catalan connections. For the case of a Catalan connection with no arc starting and ending on the same side of the tangle, we find a closed formula for its coefficient in the Relative Kauffman Bracket Skein Module of $P\\times I$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4065","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"}