{"id":"W3083295155","doi":"10.1002/rsa.20194","title":"Simple permutations mix even better","year":2007,"lang":"en","type":"article","venue":"Random Structures and Algorithms","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Winnipeg","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Combinatorics; Permutation (music); Simple (philosophy); Mathematics; Notation; Random permutation; Derangement; Parity of a permutation; Simple random sample; Discrete mathematics; Symmetric group; Cyclic permutation; Arithmetic; Physics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0003215561,0.0001958165,0.0003356737,0.00007039566,0.0001945792,0.00004736075,0.0001238207,0.00009558161,0.0000841628],"category_scores_gemma":[0.0003571086,0.000154971,0.00008063846,0.0001212386,0.00007238806,0.000100513,0.00005722237,0.0001674891,0.000004094849],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002528142,"about_ca_system_score_gemma":0.00001331148,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006773343,"about_ca_topic_score_gemma":0.000007621528,"domain_scores_codex":[0.9988333,0.00003129147,0.0003550011,0.0002183993,0.0002498098,0.0003121827],"domain_scores_gemma":[0.9985142,0.0009260426,0.0001279178,0.0002450582,0.00007100171,0.0001158045],"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":[0.0002994541,0.0001524912,0.0006641097,0.0003973562,0.0002745032,0.0001014032,0.004315022,0.00003695026,0.002448656,0.899069,0.003809849,0.08843122],"study_design_scores_gemma":[0.003164606,0.00003617245,0.0008117001,0.00001353267,0.0000513657,0.00004314619,0.0002270272,0.0004719103,0.001472394,0.9909068,0.002593966,0.0002074178],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6026475,0.0002563051,0.3939533,0.0001921946,0.0006500898,0.0005962591,0.00002928553,0.0001796985,0.00149537],"genre_scores_gemma":[0.8926153,0.00001717772,0.1063838,0.0001418895,0.0005422111,0.00001313373,0.00001162186,0.00004768869,0.0002271735],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2899678,"threshold_uncertainty_score":0.6319533,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01974014423185885,"score_gpt":0.3187092448637326,"score_spread":0.2989691006318738,"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."}}