{"paper":{"title":"On the descent polynomial of signed multipermutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zhicong Lin","submitted_at":"2013-10-24T19:48:20Z","abstract_excerpt":"Motivated by a conjecture of Savage and Visontai about the equidistribution of the descent statistic on signed permutations of the multiset $\\{1,1,2,2,\\ldots,n,n\\}$ and the ascent statistic on $(1,4,3,8,\\ldots,2n-1,4n)$-inversion sequences, we investigate the descent polynomial of the signed permutations of a general multiset. We obtain a factorial generating function formula for a $q$-analog of these descent polynomials and apply it to show that they have only real roots. Two different proofs of the conjecture of Savage and Visontai are provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6726","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"}