{"paper":{"title":"On the Enumeration of $(s,s+1,s+2)$-Core Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Jane Y.X. Yang, Michael X.X. Zhong, Robin D.P. Zhou","submitted_at":"2014-06-10T15:14:28Z","abstract_excerpt":"Anderson established a connection between core partitions and order ideals of certain posets by mapping a partition to its $\\beta$-set. In this paper, we give a characterization of the poset $P_{(s,s+1,s+2)}$ whose order ideals correspond to $(s,s+1,s+2)$-core partitions. Using this characterization, we obtain the number of $(s,s+1,s+2)$-core partitions, the maximum size and the average size of an $(s,s+1,s+2)$-core partition, confirming three conjectures posed by Amdeberhan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2583","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"}