{"id":"W136420999","doi":"","title":"Some Theorems on Generalized Stirling Numbers.","year":2001,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Stirling engine; Stirling numbers of the first kind; Stirling number; Stirling numbers of the second kind; Pure mathematics; Applied mathematics; Thermodynamics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001919525,0.001275397,0.0007440793,0.003913138,0.001219718,0.003030659,0.001375531,0.0009741426,0.01583143],"category_scores_gemma":[0.005448838,0.0004469188,0.001254006,0.003130869,0.002655973,0.005555805,0.002003732,0.003563618,0.003384766],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001533618,"about_ca_system_score_gemma":0.0006643812,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008947405,"about_ca_topic_score_gemma":0.001354613,"domain_scores_codex":[0.9992323,0.0001892092,0.00005500409,0.0001306186,0.0002838063,0.0001090526],"domain_scores_gemma":[0.9980281,0.001201586,0.0001639095,0.0002070324,0.0002578693,0.000141527],"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":[0.00001399227,0.000006539597,0.00006396444,0.00009795938,0.000009315228,0.00006224024,0.00007683694,0.0003556816,0.0003276424,0.9839225,0.005898739,0.009164616],"study_design_scores_gemma":[0.000006962693,0.00001065841,0.0001662052,0.00004275201,0.00001060888,0.0001594546,0.00004134398,0.001207106,0.0003782037,0.9761221,0.0218434,0.0000111222],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.04905273,0.04713453,0.3050079,0.009175234,0.006123213,0.0001317954,0.00194013,0.00072736,0.580707],"genre_scores_gemma":[0.6206395,0.04554213,0.1599235,0.00698272,0.009692004,0.0005916515,0.002011547,0.0007164697,0.1539004],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01583143,"threshold_uncertainty_score":0.05296147,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0663120543958205,"score_gpt":0.3360656035913274,"score_spread":0.2697535491955069,"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."}}