{"id":"W2593977626","doi":"","title":"A generalization of Stirling, Lah and harmonic numbers with some computational applications.","year":2017,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Mathematical Inequalities and Applications","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Stirling engine; Mathematics; Generalization; Stirling numbers of the first kind; Harmonic; Stirling numbers of the second kind; Stirling number; Arithmetic; Applied mathematics; Algebra over a field; Pure mathematics; Mathematical analysis; Thermodynamics; Physics; Acoustics","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":[0.0001607732,0.00009976263,0.0001881748,0.00002702795,0.0002794781,0.00006658361,0.00018883,0.00004502522,0.00002770667],"category_scores_gemma":[0.00007203811,0.00008583834,0.00002663196,0.00004521818,0.0001599766,0.0001345159,0.00006238508,0.00005993526,0.000006103538],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001558867,"about_ca_system_score_gemma":0.00003121884,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003271652,"about_ca_topic_score_gemma":0.000004724187,"domain_scores_codex":[0.9992749,0.00001857967,0.0002511769,0.0001595892,0.0001831637,0.0001125948],"domain_scores_gemma":[0.9988932,0.0001929735,0.0003045061,0.0004211741,0.0001281821,0.00005998026],"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":[0.000004121157,0.0001126231,0.0006220125,0.0001384785,0.00002613143,2.499403e-7,0.000168822,0.00001309906,0.00005447465,0.9982001,0.0004854913,0.0001744087],"study_design_scores_gemma":[0.0005145358,0.00002874458,0.0008429049,0.00003975791,0.00003527121,0.000003100744,0.00007274925,0.002349621,0.0003103199,0.9953927,0.0003065635,0.0001037294],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.971579,0.00007591103,0.02354736,0.00066448,0.00005889956,0.000652875,0.00002710071,0.00006819481,0.003326141],"genre_scores_gemma":[0.9794059,0.00001539143,0.02014878,0.00003461863,0.000009906217,0.0001375677,0.00001277697,0.0000179566,0.0002171387],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007826823,"threshold_uncertainty_score":0.3500386,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04559626980702937,"score_gpt":0.3261349824182151,"score_spread":0.2805387126111858,"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."}}