{"paper":{"title":"Group Permanents of Abelian $p$-Groups and Young Diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Naoya Yamaguchi, Yuka Yamaguchi","submitted_at":"2026-06-22T14:43:32Z","abstract_excerpt":"We study the number $\\Nu(\\Per(G_{\\lambda}))$ of distinct monomials with nonzero coefficients in the group permanent of an abelian $p$-group $G_\\lambda$ associated with a partition $\\lambda$ of a positive integer $N$. First, we derive an explicit formula for $\\Nu(\\Per(G_{\\lambda}))$ in terms of the partial column sums of the Young diagram of $\\lambda$. Next, we show that the relative order of the values $\\Nu(\\Per(G_{\\lambda}))$ is determined by a lexicographic comparison of the conjugate Young diagrams. Finally, we investigate congruence properties of $\\Nu(\\Per(G_{\\lambda}))$ for abelian $p$-gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23765","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23765/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}