{"paper":{"title":"On self-conjugate $(s, s+1,\\ldots, s+k)$-core partitions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hao Zhou, Sherry H.F. Yan, Yao Yu","submitted_at":"2019-05-02T04:36:30Z","abstract_excerpt":"Simultaneous core partitions have been widely studied since Anderson's work on the enumeration of $(s,t)$-core partitions. Amdeberhan and Leven showed that the number of $(s,s+1, \\ldots, s+k)$-core partitions is equal to the number of $(s, k)$-Dyck paths. In this paper, we prove that self-conjugate $(s,s+1, \\ldots, s+k)$-core partitions are equinumerous with symmetric $(s, k)$-Dyck paths, confirming a conjecture posed by Cho, Huh and Sohn."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00570","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":""},"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"}