{"id":"W1847349865","doi":"10.55016/ojs/cdm.v11i1.62389","title":"Diagonal recurrence relations for the Stirling numbers of the first kind","year":2016,"lang":"en","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":17,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"National Natural Science Foundation of China","keywords":"Diagonal; Stirling engine; Stirling numbers of the first kind; Stirling number; Recurrence relation; Stirling numbers of the second kind; Mathematics; Bell polynomials; Algebra over a field; Combinatorics; Pure mathematics; Physics; Geometry; Thermodynamics","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":[0.001206785,0.0008548716,0.0006265517,0.003016221,0.001309893,0.002698584,0.001038304,0.0009743441,0.009359952],"category_scores_gemma":[0.005336678,0.0003760208,0.001027054,0.00171701,0.001801898,0.003416206,0.00126905,0.002435784,0.003160884],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001380459,"about_ca_system_score_gemma":0.0005616292,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001111913,"about_ca_topic_score_gemma":0.002021403,"domain_scores_codex":[0.9990811,0.0001544096,0.0000898299,0.0001476905,0.000344906,0.0001820509],"domain_scores_gemma":[0.9983538,0.0006096953,0.0002677398,0.0001828929,0.0004769861,0.0001088502],"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":[0.00001580961,0.0000111175,0.0001245457,0.00007626163,0.000005018007,0.0001060255,0.0002298246,0.0005120016,0.001919869,0.9832381,0.00190314,0.01185821],"study_design_scores_gemma":[0.000006272177,0.0000244319,0.0002060405,0.00004977623,0.00001634066,0.0004034727,0.000103891,0.01012715,0.004095139,0.9745612,0.01035528,0.00005102335],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1040892,0.008948215,0.6309375,0.001932323,0.002778499,0.000147104,0.0004497341,0.0009646145,0.2497529],"genre_scores_gemma":[0.8124317,0.004335895,0.1345963,0.001069389,0.001453073,0.0001500187,0.0004126047,0.0006477658,0.0449033],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009359952,"threshold_uncertainty_score":0.03131217,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0292395445902785,"score_gpt":0.3350296788509379,"score_spread":0.3057901342606594,"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."}}