{"paper":{"title":"Rank and Crank Moments for Partitions without Repeated Odd Parts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chris Jennings-Shaffer","submitted_at":"2014-04-07T19:00:32Z","abstract_excerpt":"Using quasimodular forms with respect to $\\Gamma_0(4)$ we find exact relations between the M2-rank for partitions without repeated odd parts and three residual cranks. From these identities we are able to deduce various congruences mod 3 and 5 between the rank and crank moments. In turn, these congruences give congruences for $M2spt(n)$, the number of occurrences of smallest parts in the partitions of $n$ with smallest part even and without repeated odd parts, and for the higher order analog $M2spt_2(n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1883","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"}