{"id":"W4400596733","doi":"10.55016/ojs/cdm.v15i1.68111","title":"Closed formulas and identities on the Bell polynomials and falling factorials","year":2020,"lang":"en","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"National Research Foundation of Korea; National Research Foundation","keywords":"Mathematics; Expression (computer science); Falling (accident); Bessel function; Combinatorics; Bell polynomials; Pure mathematics; Mathematical analysis","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":[0.003005011,0.00145946,0.001105379,0.003424128,0.00233941,0.004381681,0.002165629,0.0022294,0.009260682],"category_scores_gemma":[0.008367628,0.0007800574,0.001704036,0.002259886,0.005226367,0.007568236,0.003091627,0.00410144,0.002698674],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001797747,"about_ca_system_score_gemma":0.001113708,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008588543,"about_ca_topic_score_gemma":0.0008959182,"domain_scores_codex":[0.9980304,0.0004246487,0.0001605279,0.0002808693,0.00079464,0.0003089862],"domain_scores_gemma":[0.9977667,0.0008169335,0.000228283,0.0003211751,0.0006703938,0.0001965762],"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":[0.000004415881,0.00000680031,0.00002652315,0.00001413481,0.000002106278,0.00004065609,0.0001118153,0.0002166424,0.0003252132,0.995565,0.0005573838,0.003129299],"study_design_scores_gemma":[0.000005212406,0.000008471276,0.00004653079,0.00001655023,0.000003556773,0.0001119208,0.00004724574,0.003874906,0.000473598,0.9927194,0.002675899,0.00001668799],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05742034,0.001661935,0.8012106,0.00149119,0.001055969,0.0001232648,0.0002345189,0.000394241,0.136408],"genre_scores_gemma":[0.5957294,0.002041543,0.3506826,0.001641765,0.001277984,0.0003774795,0.0004314136,0.0006393485,0.04717838],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009260682,"threshold_uncertainty_score":0.03098005,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06137965349062514,"score_gpt":0.3260544114094571,"score_spread":0.264674757918832,"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."}}