{"id":"W2104925482","doi":"10.37236/1495","title":"Restricted permutations, continued fractions, and Chebyshev polynomials","year":2000,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":77,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Combinatorics; Mathematics; Chebyshev polynomials; Discrete mathematics; Mathematical analysis","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":[],"consensus_categories":[],"category_scores_codex":[0.001100143,0.0001523883,0.0003715701,0.0001023678,0.0002594151,0.00006913804,0.0002407243,0.00008863187,0.0006040618],"category_scores_gemma":[0.0007157953,0.0001008381,0.0001194186,0.0003272456,0.00006942418,0.0001566672,0.00001735193,0.0005891555,0.00002276008],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001327533,"about_ca_system_score_gemma":0.0002448052,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000082293,"about_ca_topic_score_gemma":0.000003415613,"domain_scores_codex":[0.9983469,0.0002171287,0.000674722,0.00009710406,0.0002952002,0.0003689447],"domain_scores_gemma":[0.9976695,0.001409848,0.0003876936,0.0002577832,0.0001801612,0.00009502798],"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":[0.0001040268,0.0002393322,0.00006307889,0.00002400222,0.0001608799,0.000003930438,0.0004484115,0.000004705458,0.0003471339,0.9829788,0.01296622,0.002659489],"study_design_scores_gemma":[0.0009262197,0.0002919552,0.0003298476,0.00003377319,0.0002012229,0.0003744023,0.0002247083,0.00006677377,0.0004277523,0.961982,0.03501363,0.0001276754],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9850316,0.002996201,0.003803903,0.002451789,0.0002571068,0.0002640705,0.000003483778,0.00003607195,0.005155793],"genre_scores_gemma":[0.9934191,0.001694735,0.0001226931,0.00008797296,0.0001662028,0.000006183758,7.875282e-7,0.00002285426,0.004479473],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02204741,"threshold_uncertainty_score":0.6614053,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01626977213501819,"score_gpt":0.2823365822993558,"score_spread":0.2660668101643376,"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."}}