{"id":"W4385458535","doi":"10.1007/s11139-023-00762-w","title":"Equidistribution and partition polynomials","year":2023,"lang":"en","type":"article","venue":"The Ramanujan Journal","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba","funders":"Max-Planck-Institut für Mathematik in den Naturwissenschaften; Simons Foundation; Pacific Institute for the Mathematical Sciences; Vanderbilt University; National Science Foundation","keywords":"Mathematics; Ramanujan's sum; Congruence relation; Divisibility rule; Partition (number theory); Macdonald polynomials; Complement (music); Crank; Combinatorics; Orthogonal polynomials; Pure mathematics; Discrete orthogonal polynomials","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001412589,0.0008868746,0.001158412,0.002131211,0.003007721,0.003446685,0.001834343,0.001607418,0.01285944],"category_scores_gemma":[0.004762011,0.0005808715,0.000772097,0.001754903,0.005891278,0.0051765,0.00295296,0.004605771,0.002132324],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002183554,"about_ca_system_score_gemma":0.001017425,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001826598,"about_ca_topic_score_gemma":0.00142193,"domain_scores_codex":[0.9989761,0.0003149672,0.00003470974,0.0001672671,0.0002718639,0.0002351397],"domain_scores_gemma":[0.9984976,0.0005820794,0.0002110654,0.0002363931,0.0002414227,0.0002314467],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001204644,0.000007367825,0.00002446292,0.000007025756,0.000001595586,0.00001598136,0.00005949178,0.0002912766,0.0001490127,0.9977396,0.0003458411,0.001346376],"study_design_scores_gemma":[0.000006600486,0.000003943078,0.00003618933,0.000005774692,0.000001158002,0.00002250656,0.00002999566,0.002181626,0.00009473185,0.9968573,0.0007555845,0.000004622375],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4448483,0.004599345,0.1815708,0.004843104,0.001775756,0.00007488612,0.0002080652,0.0003347401,0.361745],"genre_scores_gemma":[0.9224831,0.001766326,0.01193222,0.000670746,0.0007035146,0.00008206455,0.0001558551,0.0002592626,0.06194691],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01285944,"threshold_uncertainty_score":0.04301912,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.122120037466109,"score_gpt":0.3835757315264845,"score_spread":0.2614556940603755,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}