{"paper":{"title":"The Tutte q-Polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guus Bollen, Henry Crapo, Relinde Jurrius","submitted_at":"2017-07-11T20:54:00Z","abstract_excerpt":"$q$-Matroids are defined on complemented modular support lattices. Minors of length 2 are of four types as in a \"classical\" matroid. Tutte polynomials $\\tau(x,y)$ of matroids are calculated either by recursion over deletion/contraction of single elements, by an enumeration of bases with respect to internal/external activities, or by substitution $x \\to (x-1),\\; y \\to (y-1)$ in their rank generating functions $\\rho(x,y)$. The $q$-analogue of the passage from a Tutte polynomial to its corresponding RGF is straight-forward, but the analogue of the reverse process $x \\to (x-1),\\; y \\to (y-1)$ is m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03459","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"}