{"id":"W2950502640","doi":"10.1007/s00026-011-0119-0","title":"Words and Polynomial Invariants of Finite Groups in Non-Commutative Variables","year":2011,"lang":"en","type":"article","venue":"Annals of Combinatorics","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal; York University","funders":"","keywords":"Commutative property; Polynomial; Mathematics; Polynomial ring; Algebra over a field; Pure mathematics; Computer science; 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":[0.002063251,0.0009473577,0.001550881,0.003970035,0.003062897,0.005713441,0.002118581,0.001269355,0.006377841],"category_scores_gemma":[0.004715701,0.000811221,0.001397397,0.003774169,0.009132392,0.0124489,0.00307362,0.003382349,0.0007941505],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002533332,"about_ca_system_score_gemma":0.001107118,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001915583,"about_ca_topic_score_gemma":0.002081904,"domain_scores_codex":[0.9984089,0.0003883586,0.0001010695,0.0003341577,0.0003213885,0.0004462578],"domain_scores_gemma":[0.9955848,0.002555052,0.000724183,0.0003634144,0.000303645,0.0004689536],"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":[0.00005420788,0.00003375555,0.0003146254,0.00002218388,0.000007201928,0.00005863802,0.0006207243,0.0006065049,0.0002777335,0.9950912,0.0002842702,0.002628958],"study_design_scores_gemma":[0.00001795837,0.00001343321,0.0001936848,0.000005779387,0.00001160222,0.00003206727,0.0001521154,0.001263116,0.0002428318,0.9974329,0.0006245865,0.000009961803],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8384377,0.002200038,0.1070477,0.002884267,0.0003910382,0.00006276183,0.0003674323,0.00035564,0.04825348],"genre_scores_gemma":[0.9822398,0.0005889949,0.006915936,0.0001941967,0.0005723685,0.00004526667,0.0002587538,0.00006851608,0.009116235],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006377841,"threshold_uncertainty_score":0.02133602,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.164123959274459,"score_gpt":0.3583939399102883,"score_spread":0.1942699806358293,"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."}}