{"id":"W4400596798","doi":"10.55016/ojs/cdm.v15i3.68674","title":"On the uniformity of the approximation for $r$-associated Stirling numbers of the second Kind","year":2020,"lang":"en","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Stirling numbers of the second kind; Stirling numbers of the first kind; Stirling number; Mathematics; Stirling engine; Bell polynomials; Extension (predicate logic); Range (aeronautics); Generating function; Partition (number theory); Combinatorics; Function (biology); Spouge's approximation; Natural number; Discrete mathematics; Applied mathematics; Minimax approximation algorithm; Computer science; Physics","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":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.0008210148,0.0002309132,0.0005033903,0.00003169408,0.0003859185,0.00004048667,0.0008113406,0.0001100105,0.00009702729],"category_scores_gemma":[0.02336362,0.0001181377,0.0003839319,0.0005631499,0.0002810186,0.00009862886,0.0002829046,0.0002521202,0.000008674207],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001270845,"about_ca_system_score_gemma":0.00009048664,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000225993,"about_ca_topic_score_gemma":0.00003561475,"domain_scores_codex":[0.9979779,0.0001313771,0.000873491,0.0001912828,0.0005195405,0.0003064168],"domain_scores_gemma":[0.9940324,0.003759807,0.0008395253,0.0007786746,0.0005095595,0.00007999562],"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":[0.00001575546,0.0001424137,0.00001872351,0.0006245598,0.0001069926,6.486184e-8,0.003221469,0.0001640777,0.001641425,0.9913152,0.002737787,0.00001148155],"study_design_scores_gemma":[0.0004906455,0.00006412032,0.00006654236,0.0004459961,0.0001990793,0.000001128477,0.001776094,0.009206893,0.03689484,0.950489,0.0002099366,0.000155662],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5775784,0.00002775939,0.3936993,0.01364577,0.0002580041,0.006330242,0.003105073,0.000120467,0.005234962],"genre_scores_gemma":[0.989737,0.000001002857,0.0086352,0.0002704776,0.00003831125,0.0001711709,0.000008373842,0.00004057785,0.001097921],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4121585,"threshold_uncertainty_score":0.984863,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03972416383204305,"score_gpt":0.3168064005049099,"score_spread":0.2770822366728668,"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."}}