{"id":"W1521513823","doi":"10.37236/1133","title":"Cycle Lengths in a Permutation are Typically Poisson","year":2006,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Mathematics; Permutation (music); Combinatorics; Poisson distribution; Set (abstract data type); Order (exchange); Parity of a permutation; Prime (order theory); Permutation group; Discrete mathematics; Cyclic permutation; Symmetric group; Statistics; Computer science","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":[0.0009297436,0.000130471,0.0003111208,0.0001166954,0.00006872916,0.00003471064,0.0003301534,0.00006415128,0.00001770913],"category_scores_gemma":[0.0006776037,0.00009205253,0.0001036712,0.0003017499,0.00005397146,0.0002124732,0.00003412374,0.0006152221,0.00000957559],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004524352,"about_ca_system_score_gemma":0.0001371896,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008036529,"about_ca_topic_score_gemma":0.00005818695,"domain_scores_codex":[0.9983637,0.0001162302,0.0005987554,0.0000816951,0.0004260035,0.0004135538],"domain_scores_gemma":[0.9983355,0.0006838806,0.0005551209,0.0001899646,0.0002029459,0.00003252594],"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":[0.00003180864,0.0002541644,0.000171456,0.00003487226,0.00001682172,0.00001404904,0.0001882726,0.000127203,0.000139379,0.998449,0.0005274019,0.00004553914],"study_design_scores_gemma":[0.0007166632,0.0001425692,0.0006792315,0.0000638071,0.00004105374,0.0001067617,0.0003325382,0.0001846522,0.0005701487,0.9967481,0.0003156202,0.00009883923],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9680746,0.001544396,0.02541916,0.001683978,0.0001927064,0.0001894591,6.674953e-7,0.00003109218,0.002864006],"genre_scores_gemma":[0.9985607,0.0001093097,0.0001990314,0.00002493623,0.00008743183,0.000003726699,3.090871e-7,0.00002561878,0.0009889432],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03048616,"threshold_uncertainty_score":0.3753793,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01032394521202556,"score_gpt":0.2784055045512657,"score_spread":0.2680815593392402,"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."}}