{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006503853,0.0006340639,0.0004942568,0.001621886,0.001004398,0.001606301,0.0004885896,0.0006980937,0.003154634],"category_scores_gemma":[0.002872947,0.00027204,0.0005829366,0.001406802,0.002379975,0.002154285,0.0009622803,0.001297399,0.0008099608],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001366354,"about_ca_system_score_gemma":0.0006637277,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002819088,"about_ca_topic_score_gemma":0.002096745,"domain_scores_codex":[0.9995528,0.0001238421,0.00001855508,0.00007039414,0.0001198799,0.0001144499],"domain_scores_gemma":[0.9993131,0.0003259765,0.000130342,0.00009828682,0.00006940891,0.00006281861],"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":[0.00003452392,0.000008960235,0.0002023582,0.00001817686,0.000003526518,0.00006625474,0.00009232536,0.002458788,0.0009322291,0.9873106,0.0004313176,0.008440932],"study_design_scores_gemma":[0.0000131127,0.00001808326,0.0002856948,0.00001390523,0.000005242563,0.000148734,0.00003347501,0.0132714,0.0007543968,0.9818326,0.003607971,0.00001523638],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6670122,0.005702694,0.2105976,0.002122263,0.0003366716,0.00006105135,0.0003220565,0.0003343821,0.1135111],"genre_scores_gemma":[0.9616528,0.002093468,0.01771103,0.0002221624,0.0003736498,0.00007385449,0.000161196,0.00006407099,0.01764783],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003154634,"threshold_uncertainty_score":0.0105533,"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."}}