{"paper":{"title":"The $\\mu$-permanent revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carlos M. da Fonseca","submitted_at":"2018-04-06T12:28:20Z","abstract_excerpt":"Let $A=(a_{ij})$ be an $n$-by-$n$ matrix. For any real number $\\mu$, we define the polynomial $$P_\\mu(A)=\\sum_{\\sigma\\in S_n} a_{1\\sigma(1)}\\cdots a_{n\\sigma(n)}\\,\\mu^{\\ell(\\sigma)}\\; ,$$ as the $\\mu$-permanent of $A$, where $\\ell(\\sigma)$ is the number of inversions of the permutation $\\sigma$ in the symmetric group $S_n$. In this note, we review several less known results of the $\\mu$-permanent, recalling some of its interesting properties. Some determinantal conjectures are considered and extended to that polynomial. A correction to a previous note is presented as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02231","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"}