{"id":"W2031777414","doi":"10.4153/cjm-2008-013-4","title":"Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables","year":2008,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":59,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal; York University","funders":"","keywords":"Noncommutative geometry; Mathematics; Hopf algebra; Quantum group; Noncommutative algebraic geometry; Symmetric algebra; Subspace topology; Algebra over a field; Pure mathematics; Combinatorics; Cellular algebra; Noncommutative quantum field theory; Algebra representation; Mathematical analysis","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":[0.00124623,0.0003371323,0.000691027,0.001751461,0.001099367,0.002142569,0.0006000355,0.0003937063,0.00438242],"category_scores_gemma":[0.001366585,0.0001896892,0.0004195621,0.001034006,0.004523093,0.0034387,0.002108243,0.0008297837,0.0003326788],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009684441,"about_ca_system_score_gemma":0.0006507852,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001294336,"about_ca_topic_score_gemma":0.00108608,"domain_scores_codex":[0.9991884,0.000145039,0.00005161068,0.000136365,0.000289109,0.0001895446],"domain_scores_gemma":[0.9990842,0.000187829,0.0001657098,0.0001422896,0.0001762189,0.0002436638],"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":[0.0000182103,0.00001885401,0.0003509148,0.000008154633,0.000004431598,0.00008582683,0.0002556134,0.0004639816,0.001185467,0.9949521,0.0001234554,0.002533073],"study_design_scores_gemma":[0.00001624118,0.00004723256,0.001105269,0.000007678054,0.000009965255,0.0001281151,0.0002947318,0.004940166,0.002243161,0.9890259,0.002161355,0.0000201574],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9164912,0.0004630206,0.05551624,0.0003175963,0.0002266806,0.00003822143,0.00009239989,0.00009205168,0.02676255],"genre_scores_gemma":[0.9936237,0.0001575708,0.001918794,0.00004873319,0.00008641268,0.00001528501,0.00005677847,0.00001589669,0.0040768],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00438242,"threshold_uncertainty_score":0.01466072,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04119192290728407,"score_gpt":0.2389146209438533,"score_spread":0.1977226980365692,"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."}}