{"id":"W2276776477","doi":"10.37236/5949","title":"Antipode Formulas for some Combinatorial Hopf Algebras","year":2016,"lang":"en","type":"preprint","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Noncommutative geometry; Bialgebra; Hopf algebra; Mathematics; Symmetric function; Grassmannian; Combinatorics; Pure mathematics; Algebra over a field","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","research_integrity"],"consensus_categories":[],"category_scores_codex":[0.004476992,0.001020853,0.002176677,0.0003847583,0.0004722127,0.0001776417,0.003408828,0.0007058571,0.00001416887],"category_scores_gemma":[0.003764874,0.0006659128,0.001308067,0.0003462939,0.0002434136,0.0004620008,0.001013573,0.00331073,0.00001223927],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001991329,"about_ca_system_score_gemma":0.002528439,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001772803,"about_ca_topic_score_gemma":0.000001340979,"domain_scores_codex":[0.9930836,0.0004010938,0.002461607,0.0005301474,0.001649295,0.001874282],"domain_scores_gemma":[0.9869397,0.00474936,0.004693857,0.00175409,0.001588308,0.0002746624],"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":[0.0003960734,0.0006001645,0.000007452677,0.0005432653,0.0008221858,0.00001358759,0.0003203267,0.0000150133,0.0001553249,0.9915531,0.005244777,0.0003286719],"study_design_scores_gemma":[0.005357373,0.001361571,0.000001990152,0.0006604549,0.0008907047,0.0001771816,0.00007643264,0.0001072864,0.004476573,0.9790239,0.007101222,0.0007652742],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3758177,0.01526054,0.5269933,0.006822427,0.06520664,0.007352513,0.0001528845,0.0005360928,0.00185793],"genre_scores_gemma":[0.9933866,0.001482283,0.0007271044,0.00008295216,0.00328839,0.0001178146,0.000006707091,0.0003388298,0.0005693302],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6175689,"threshold_uncertainty_score":0.9995792,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02960561380730311,"score_gpt":0.3183074453619741,"score_spread":0.288701831554671,"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."}}