{"paper":{"title":"Enumeration on row-increasing tableaux of shape $2 \\times n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rosena R. X. Du, Xiaojie Fan, Yue Zhao","submitted_at":"2018-03-05T10:31:04Z","abstract_excerpt":"Recently O. Pechenik studied the cyclic sieving of increasing tableaux of shape $2\\times n$, and obtained a polynomial on the major index of these tableaux, which is a $q$-analogue of refined small Schr\\\"{o}der numbers. We define row-increasing tableaux and study the major index and amajor index of row-increasing tableaux of shape $2 \\times n$. The resulting polynomials are both $q$-analogues of refined large Schr\\\"{o}der numbers. For both results we give bijective proofs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01590","kind":"arxiv","version":4},"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"}