{"paper":{"title":"On the density of the odd values of the partition function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.NT"],"primary_cat":"math.CO","authors_text":"Fabrizio Zanello, Samuel D. Judge, William J. Keith","submitted_at":"2015-11-17T20:11:16Z","abstract_excerpt":"The purpose of this note is to introduce a new approach to the study of one of the most basic and seemingly intractable problems in partition theory, namely the conjecture that the partition function $p(n)$ is equidistributed modulo 2.\n  Our main result will relate the densities, say $\\delta_t$, of the odd values of the $t$-multipartition functions $p_t(n)$, for several integers $t$. In particular, we will show that if $\\delta_t>0$ for some $t\\in \\{5,7,11,13,17,19,23,25\\}$, then (assuming it exists) $\\delta_1>0$; that is, $p(n)$ itself is odd with positive density. Notice that, currently, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05531","kind":"arxiv","version":2},"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"}