{"paper":{"title":"Proof of the Refined Alternating Sign Matrix Conjecture","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Doron Zeilberger (Temple University)","submitted_at":"1996-06-03T19:29:36Z","abstract_excerpt":"Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order $n$ equals $A(n):={{1!4!7! ... (3n-2)!} \\over {n!(n+1)! ... (2n-1)!}}$. Mills, Robbins, and Rumsey also made the stronger conjecture that the number of such matrices whose (unique) `1' of the first row is at the $r^{th}$ column, equals $A(n) {{n+r-2} \\choose {n-1}}{{2n-1-r} \\choose {n-1}}/ {{3n-2} \\choose {n-1}}$. Standing on the shoulders of A.G. Izergin, V. E. Korepin, and G. Kuperberg, and using in addition orthogonal polynomials and $q$-calculus, this stronger conjecture is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9606224","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/9606224/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}