{"paper":{"title":"Hamming Polynomial of a Demimatroid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Jose Martinez-Bernal, Miguel A. Valencia-Bucio, Rafael H. Villarreal","submitted_at":"2019-07-23T01:02:46Z","abstract_excerpt":"Following Britz, Johnsen, Mayhew and Shiromoto, we consider demi\\-ma\\-troids as a(nother) natural generalization of matroids. As they have shown, demi\\-ma\\-troids are the appropriate combinatorial objects for studying Wei's duality. Our results here apport further evidence about the trueness of that observation. We define the Hamming polynomial of a demimatroid $M$, denoted by $W(x,y,t)$, as a generalization of the extended Hamming weight enumerator of a matroid. The polynomial $W(x,y,t)$ is a specialization of the Tutte polynomial of $M$, and actually is equivalent to it. Guided by work of Jo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09644","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"}