{"id":"W2992045920","doi":"10.1007/s00029-021-00721-7","title":"Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials","year":2022,"lang":"en","type":"article","venue":"Selecta Mathematica","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Macdonald polynomials; Koornwinder polynomials; Mathematics; Orthogonal polynomials; Askey–Wilson polynomials; Classical orthogonal polynomials; Discrete orthogonal polynomials; Schur polynomial; Difference polynomials; Wilson polynomials; Combinatorics; Jacobi polynomials; Pure mathematics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001886573,0.0006586433,0.001426293,0.0005621326,0.0009085916,0.0001531191,0.0008304518,0.0001528851,0.00068786],"category_scores_gemma":[0.003222596,0.0006446793,0.000367131,0.001025424,0.0001242573,0.0002733028,0.000440947,0.0004914211,0.00004849759],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004251312,"about_ca_system_score_gemma":0.0001701541,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001024986,"about_ca_topic_score_gemma":0.000005621122,"domain_scores_codex":[0.9955987,0.0002480702,0.00139067,0.0007427405,0.0009542336,0.001065632],"domain_scores_gemma":[0.9914785,0.006221117,0.000843814,0.0009485192,0.000188932,0.000319137],"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":[0.0002783986,0.001095876,0.00006710075,0.001496166,0.0003692159,0.00001078921,0.001346697,0.00001186075,0.003120521,0.9429526,0.04717717,0.002073571],"study_design_scores_gemma":[0.002381765,0.0006786535,0.00002173434,0.00008267724,0.0003147505,0.0002098418,0.0005056207,0.003360196,0.004596819,0.9738064,0.01319846,0.0008430924],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8132417,0.003232429,0.1008934,0.01031584,0.003754389,0.02101153,0.001688292,0.002783509,0.04307897],"genre_scores_gemma":[0.9017065,0.00003597416,0.0921166,0.00045248,0.0004043249,0.0009963233,0.00003893719,0.0003362405,0.003912685],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0884648,"threshold_uncertainty_score":0.9996005,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0547373483301812,"score_gpt":0.3346324921792909,"score_spread":0.2798951438491097,"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."}}