{"paper":{"title":"Alternating sum formulae for the determinant and other link invariants","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"David Futer, Efstratia Kalfagianni, Neal W. Stoltzfus, Oliver T. Dasbach, Xiao-Song Lin","submitted_at":"2006-11-01T17:44:22Z","abstract_excerpt":"A classical result states that the determinant of an alternating link is equal to the number of spanning trees in a checkerboard graph of an alternating connected projection of the link.\n  We generalize this result to show that the determinant is the alternating sum of the number of quasi-trees of genus j of the dessin of a non-alternating link.\n  Furthermore, we obtain formulas for other link invariants by counting quantities on dessins. In particular we will show that the $j$-th coefficient of the Jones polynomial is given by sub-dessins of genus less or equal to $j$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611025","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"}