{"paper":{"title":"Exotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and Bailey Pairs From Groups A, C, E","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chris Jennings-Shaffer, Frank Garvan","submitted_at":"2015-01-27T17:52:26Z","abstract_excerpt":"We investigate spt-crank-type functions arising from Bailey pairs. We recall four spt-type functions corresponding to the Bailey pairs $A1$, $A3$, $A5$, and $A7$ of Slater and given four new spt-type functions corresponding to Bailey pairs $C1$, $C5$, $E2$, and $E4$. Each of these functions can be thought of as a count on the number of appearances of the smallest part in certain integer partitions. We prove simple Ramanujan type congruences for these functions that are explained by a spt-crank-type function. The spt-crank-type functions are two variable $q$-series determined by a Bailey pair, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06843","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"}