{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008876231,0.0004425407,0.0004030944,0.002388978,0.001292913,0.00321079,0.0008888863,0.000807182,0.006930271],"category_scores_gemma":[0.002598035,0.0003724163,0.0004984895,0.001479422,0.002176192,0.005154036,0.001209877,0.002072948,0.0008794642],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001315719,"about_ca_system_score_gemma":0.0005295552,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004561617,"about_ca_topic_score_gemma":0.0005773,"domain_scores_codex":[0.9994727,0.0001092888,0.00004707075,0.00007437231,0.0002279855,0.00006868599],"domain_scores_gemma":[0.9990016,0.0003916022,0.0001269403,0.00007879076,0.0002844683,0.0001166409],"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":[0.000004978111,0.000008713408,0.0000871692,0.00001223949,0.000001610199,0.00006197289,0.0000928515,0.0001695445,0.0003345714,0.9966493,0.0002335518,0.002343571],"study_design_scores_gemma":[0.00000695256,0.000006802582,0.000106463,0.00000748339,0.000002735652,0.0001046199,0.00006036944,0.002636795,0.0005089875,0.9942672,0.002284531,0.000007097277],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5444227,0.002285762,0.242591,0.002199417,0.0005236253,0.0001528083,0.000508085,0.0002806145,0.207036],"genre_scores_gemma":[0.9512259,0.0008060577,0.02929717,0.0003432088,0.0003337192,0.0001133914,0.0002678991,0.00006059953,0.01755211],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006930271,"threshold_uncertainty_score":0.02318406,"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."}}