{"id":"W123151599","doi":"","title":"Asymptotic Normality of the (r, beta)-Stirling Numbers.","year":2006,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Cold Atom Physics and Bose-Einstein Condensates","field":"Physics and Astronomy","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; BETA (programming language); Stirling numbers of the first kind; Normality; Stirling engine; Stirling numbers of the second kind; Beta distribution; Stirling number; Combinatorics; Statistics; Computer science; Thermodynamics; Physics; Programming language","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001202494,0.0001452812,0.0002010412,0.00001734793,0.0001497701,0.00003581411,0.0002887851,0.00003077319,0.0001208164],"category_scores_gemma":[0.000002598102,0.0001128844,0.0001860469,0.0002243859,0.00008063706,0.00009154306,0.0001263894,0.0001436789,0.00002298636],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001981253,"about_ca_system_score_gemma":0.0000528056,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0014089,"about_ca_topic_score_gemma":0.00001484541,"domain_scores_codex":[0.9990606,0.00004265918,0.0002716843,0.0001818466,0.0002165414,0.0002267212],"domain_scores_gemma":[0.9992374,0.00008314575,0.0001700286,0.0003899192,0.00008498684,0.00003459013],"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":[0.000002087455,0.0001284379,0.2840994,0.000008384327,0.00002848835,2.555589e-7,0.00003600065,0.00003831249,0.001609166,0.7130678,0.0004425854,0.0005390547],"study_design_scores_gemma":[0.0007941181,0.00002191346,0.1228788,0.00004384645,0.00005975274,3.434808e-7,0.00007457165,0.000268481,0.05395744,0.8198823,0.001775161,0.0002433044],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9687783,0.00003647276,0.00001650864,0.0001270372,0.0008079908,0.0001436884,0.00001572289,0.00002039089,0.0300539],"genre_scores_gemma":[0.9994162,3.065823e-7,0.00002901576,0.00001981411,0.00005452678,0.000008136637,0.00001036051,0.00001462998,0.0004469887],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1612206,"threshold_uncertainty_score":0.4603293,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.005654705986215781,"score_gpt":0.2077956210617751,"score_spread":0.2021409150755593,"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."}}