{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001619407,0.0001876085,0.0003810019,0.0001352486,0.0001084732,0.00002559688,0.0003298102,0.00007726511,0.000008345405],"category_scores_gemma":[0.001950151,0.0001387474,0.00007566877,0.0004638003,0.00007749385,0.0001839883,0.00003262669,0.0008901128,0.000003548395],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003044462,"about_ca_system_score_gemma":0.0002726196,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002571401,"about_ca_topic_score_gemma":0.00001076993,"domain_scores_codex":[0.9980793,0.0002690132,0.000657426,0.0001199042,0.0003893342,0.0004850357],"domain_scores_gemma":[0.997763,0.00113829,0.0005469456,0.0002841594,0.0002013643,0.0000662366],"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":[0.00001174682,0.000180537,0.0004239132,0.00004020272,0.00003601262,0.00000973869,0.0007730316,0.00004524222,0.00006995186,0.9981195,0.00005673195,0.0002333625],"study_design_scores_gemma":[0.001374826,0.0002520782,0.00006240735,0.00007146324,0.00004579561,0.0002344411,0.0004954939,0.0001753311,0.000569866,0.9955337,0.001039537,0.0001450649],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9073142,0.002783072,0.08785549,0.0005671337,0.0005312842,0.0002957392,5.156798e-7,0.00002319809,0.0006293137],"genre_scores_gemma":[0.9987535,0.0006471616,0.0003570094,0.0000501038,0.00004076607,0.000006612757,1.349926e-7,0.00003694283,0.0001077974],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09143922,"threshold_uncertainty_score":0.5657957,"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."}}