{"id":"W3102170734","doi":"","title":"Combinatorial Hopf algebras and generalized DehnSommerville relations","year":2012,"lang":"en","type":"article","venue":"","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":216,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"","keywords":"Hopf algebra; Mathematics; Subalgebra; Quasitriangular Hopf algebra; Division algebra; Quantum group; Pure mathematics; Representation theory of Hopf algebras; Cross product; Combinatorics; 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":[0.0004256469,0.0002547365,0.0002176554,0.001087331,0.0007791978,0.001096864,0.0003912268,0.0002891391,0.003185954],"category_scores_gemma":[0.0007459518,0.0001103235,0.0003704171,0.0007166239,0.001300256,0.001999341,0.0009516625,0.0005706246,0.0003229278],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00079546,"about_ca_system_score_gemma":0.000316461,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000795258,"about_ca_topic_score_gemma":0.001510077,"domain_scores_codex":[0.9997109,0.00005655572,0.00001916933,0.00004730665,0.0001077166,0.00005839218],"domain_scores_gemma":[0.999698,0.00005530246,0.00006360832,0.00005057571,0.00007179851,0.00006071083],"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":[0.00001389115,0.000009752192,0.0005842358,0.00001612562,0.000004024618,0.00008070519,0.0001217814,0.0007627691,0.001813957,0.9921516,0.0002408528,0.004200389],"study_design_scores_gemma":[0.000009745795,0.00002340329,0.00120388,0.0000116355,0.000009064151,0.0002309238,0.0001542603,0.007543701,0.00319754,0.981649,0.005951245,0.00001561699],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7932872,0.001078328,0.09431385,0.0005732162,0.0001205108,0.0000556379,0.0001946793,0.0001712608,0.1102053],"genre_scores_gemma":[0.9817466,0.0002354438,0.009204474,0.0001039349,0.00005906919,0.0000308965,0.0001113267,0.00001693844,0.008491208],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003185954,"threshold_uncertainty_score":0.01065809,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04336775232026355,"score_gpt":0.3165602809370492,"score_spread":0.2731925286167857,"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."}}