{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001581386,0.0004007547,0.0008484696,0.001839064,0.001255692,0.003037296,0.001261948,0.0007299418,0.003109583],"category_scores_gemma":[0.01221837,0.0005415172,0.0005634868,0.001905351,0.003581038,0.005435985,0.001644448,0.00147922,0.0005055939],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001261208,"about_ca_system_score_gemma":0.0006244206,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004120044,"about_ca_topic_score_gemma":0.000346132,"domain_scores_codex":[0.9974689,0.0004138428,0.0001501316,0.0008471428,0.0008425567,0.0002772925],"domain_scores_gemma":[0.9910195,0.004675014,0.001552585,0.001431966,0.00087774,0.0004430995],"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":[0.0001060713,0.00002651172,0.003545317,0.00009130304,0.00004072828,0.0001791581,0.0004183941,0.006424125,0.00439156,0.9645548,0.00201761,0.01820442],"study_design_scores_gemma":[0.00001446892,0.00002857629,0.001382252,0.00002234801,0.0000192125,0.0004707403,0.0001380935,0.02283961,0.002948732,0.9667034,0.005402,0.00003054535],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6007503,0.0008903521,0.3590428,0.001472811,0.0001963203,0.00008061827,0.0006284269,0.0006232766,0.03631521],"genre_scores_gemma":[0.9726512,0.0007569905,0.01988021,0.0003538586,0.0003573089,0.0001861996,0.0003958884,0.0001505222,0.005267721],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003109583,"threshold_uncertainty_score":0.01040256,"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."}}