{"id":"W2056514476","doi":"10.1016/j.jcta.2005.11.005","title":"On the number of factorizations of a full cycle","year":2006,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series A","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":22,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Algebraic number; Argument (complex analysis); Product (mathematics); Expression (computer science); Algebraic expression; Combinatorics; Algebra over a field; Pure mathematics; Computer science; Chemistry; Geometry","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002790529,0.001001137,0.001674531,0.003156896,0.00441742,0.006456567,0.002406014,0.002686483,0.01856323],"category_scores_gemma":[0.01886159,0.001085657,0.001397945,0.001920196,0.004840754,0.0104208,0.003027908,0.002840236,0.001446818],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001867443,"about_ca_system_score_gemma":0.001355371,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001632996,"about_ca_topic_score_gemma":0.001899595,"domain_scores_codex":[0.9976093,0.0005045899,0.0001661594,0.0006138707,0.0005315674,0.0005745685],"domain_scores_gemma":[0.9801955,0.01216572,0.001981095,0.001502511,0.001440272,0.002714994],"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":[0.001802465,0.0002166929,0.007244276,0.0003672444,0.0001195989,0.0003163812,0.0009470531,0.01037653,0.006311815,0.927515,0.01147888,0.03330415],"study_design_scores_gemma":[0.0001276925,0.000139406,0.002009807,0.0001209298,0.00009117575,0.0005205854,0.0003964212,0.02278865,0.001776347,0.9664646,0.005492576,0.00007173543],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8590857,0.001751892,0.06221937,0.004447545,0.0005694836,0.0001460427,0.001998794,0.0004498518,0.06933118],"genre_scores_gemma":[0.9670364,0.0006093919,0.01979834,0.0003576248,0.0003878816,0.000125316,0.001233935,0.0001269281,0.01032415],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01856323,"threshold_uncertainty_score":0.06210023,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01468624669388858,"score_gpt":0.2848291925960306,"score_spread":0.270142945902142,"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."}}