{"id":"W2994065064","doi":"10.37236/1690","title":"Pattern Avoidance in Permutations: Linear and Cyclic Orders","year":2003,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Chalmers Tekniska Högskola","keywords":"Mathematics; Bijection, injection and surjection; Combinatorics; Generating function; Euler's totient function; Lemma (botany); Permutation (music); Simple (philosophy); Bijection; Discrete mathematics; Euler's formula","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":[0.0004797026,0.0003249212,0.0002970177,0.001004118,0.0007949648,0.001617984,0.0005572254,0.0006112815,0.003072494],"category_scores_gemma":[0.002585188,0.0001890742,0.0004327192,0.001068246,0.001727349,0.002300668,0.001157099,0.0007672906,0.0003692535],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008839066,"about_ca_system_score_gemma":0.0004677064,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001059006,"about_ca_topic_score_gemma":0.00103957,"domain_scores_codex":[0.9994184,0.000108464,0.00003919332,0.0001013315,0.0001904581,0.0001421652],"domain_scores_gemma":[0.9984069,0.000712849,0.0002531367,0.0003250408,0.0001639877,0.0001380024],"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":[0.00004999786,0.00002008317,0.001858212,0.00003364762,0.000005777867,0.0001800684,0.0002867008,0.005994416,0.002649858,0.9699803,0.0007467104,0.01819422],"study_design_scores_gemma":[0.0000172467,0.0000448135,0.001270824,0.00002145192,0.000009928308,0.0005333168,0.0001792191,0.03908081,0.002847901,0.9474866,0.008483402,0.00002438439],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7224842,0.0005339794,0.2201903,0.0005922405,0.0000700687,0.00005331299,0.0002744026,0.0001879617,0.05561344],"genre_scores_gemma":[0.9774331,0.0002973788,0.01504186,0.00009048729,0.00006067942,0.00005123529,0.0001514687,0.00004796514,0.00682585],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003072494,"threshold_uncertainty_score":0.01027852,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01831435443319612,"score_gpt":0.2991734189737368,"score_spread":0.2808590645405407,"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."}}