{"id":"W4400196807","doi":"10.5070/c64163853","title":"The primitive Eulerian polynomial","year":2024,"lang":"en","type":"article","venue":"Combinatorial Theory","topic":"Mathematics and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Eulerian path; Polynomial; Mathematics; Computer science; Pure mathematics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003078986,0.0004171883,0.000332248,0.001213632,0.0006737708,0.001287984,0.0005333925,0.0003580063,0.01082511],"category_scores_gemma":[0.001489005,0.0001499656,0.0003089018,0.0008452929,0.002131862,0.002366342,0.001337602,0.001413129,0.001919058],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009983183,"about_ca_system_score_gemma":0.0005978554,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001413613,"about_ca_topic_score_gemma":0.001272051,"domain_scores_codex":[0.999657,0.00004171396,0.00001016656,0.00008015557,0.0001028567,0.0001081202],"domain_scores_gemma":[0.9994562,0.0001200289,0.00009892374,0.00008205447,0.0001284337,0.0001143216],"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":[0.00001731786,0.000005995597,0.0005253234,0.00002534478,0.000002094429,0.00005404283,0.0001357145,0.0009727756,0.001441584,0.9857944,0.0007853436,0.01024004],"study_design_scores_gemma":[0.000008676731,0.00004219881,0.00157592,0.00002898722,0.00000726657,0.0003500199,0.0001570111,0.0098455,0.002379307,0.9514893,0.03408749,0.0000282549],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5773329,0.001906973,0.1884863,0.001810202,0.0006249601,0.000058689,0.000850336,0.0003749095,0.2285547],"genre_scores_gemma":[0.9555324,0.0006724013,0.01990989,0.0001672019,0.0001866404,0.00001897039,0.000278303,0.00009157297,0.02314258],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01082511,"threshold_uncertainty_score":0.03621364,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03012577469032673,"score_gpt":0.3274828436840979,"score_spread":0.2973570689937712,"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."}}