{"paper":{"title":"Disturbing the Dyson conjecture in a \\emph{generally} GOOD way","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew V. Sills","submitted_at":"2018-12-13T18:16:19Z","abstract_excerpt":"Dyson's celebrated constant term conjecture ({\\em J. Math. Phys.}, 3 (1962): 140--156) states that the constant term in the expansion of $\\prod_{1\\leqq i\\neq j\\leqq n} (1-x_i/x_j)^{a_j}$ is the multinomial coefficient $(a_1 + a_2 + \\cdots + a_n)!/ (a_1! a_2! \\cdots a_n!)$. The definitive proof was given by I. J. Good ({\\em J. Math. Phys.}, 11 (1970) 1884). Later, Andrews extended Dyson's conjecture to a $q$-analog ({\\em The Theory and Application of Special Functions}, (R. Askey, ed.), New York: Academic Press, 191--224, 1975.) In this paper, closed form expressions are given for the coefficie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05557","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"}