{"id":"W2395430777","doi":"","title":"A summation formula related to q-Eulerian polynomials.","year":2010,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Eulerian path; Pure mathematics; Lagrangian","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":[0.0003973041,0.0001915741,0.0003029839,0.0001232566,0.0001307905,0.00008026021,0.0002981013,0.0001560979,0.0003383266],"category_scores_gemma":[0.001783493,0.0001864762,0.00008549896,0.0002658001,0.00005610218,0.000327452,0.0001310941,0.000300405,0.0005872698],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005244292,"about_ca_system_score_gemma":0.00003226098,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001244344,"about_ca_topic_score_gemma":0.00003795052,"domain_scores_codex":[0.9986313,0.00003425114,0.0004667338,0.0002444582,0.0002881793,0.0003350502],"domain_scores_gemma":[0.9985701,0.0004014171,0.0001367612,0.0005866056,0.0001218684,0.0001832076],"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":[0.000008842583,0.0000998375,0.0000698874,0.00004613255,0.00001831393,0.000004076562,0.0006527183,6.076307e-7,0.01115583,0.9835135,0.004159139,0.0002711029],"study_design_scores_gemma":[0.0005148747,0.00004941142,0.0001974522,0.00003703987,0.0000217049,0.000009971366,0.0001018238,0.00008075419,0.010349,0.9863786,0.002036079,0.0002233001],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9748284,0.000007486768,0.0002700018,0.0004937064,0.002258005,0.0005058952,0.000005014448,0.0003335552,0.02129789],"genre_scores_gemma":[0.9794577,0.000001598409,0.0146764,0.00005712369,0.000015086,0.00006322563,0.000005479046,0.00005785733,0.005665464],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01563243,"threshold_uncertainty_score":0.7604278,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01847527406629998,"score_gpt":0.3068029156784333,"score_spread":0.2883276416121333,"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."}}