{"id":"W2030719845","doi":"10.46298/dmtcs.2720","title":"Words and polynomial invariants of finite groups in non-commutative variables","year":2009,"lang":"en","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal; York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Subalgebra; Mathematics; Group (periodic table); Algebra homomorphism; Homomorphism; Group algebra; Finite group; Cellular algebra; Algebra over a field; Combinatorics; Pure mathematics; Discrete mathematics; Algebra representation","routes":{"ca_aff":true,"ca_fund":true,"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","sts"],"consensus_categories":[],"category_scores_codex":[0.004531042,0.0003169784,0.0006800443,0.0004848952,0.0001923121,0.000201731,0.001261872,0.0001168533,0.00009032389],"category_scores_gemma":[0.001718406,0.0002547964,0.00008083666,0.001303316,0.003446648,0.0003916685,0.0006995754,0.0004276987,0.00001163826],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005730466,"about_ca_system_score_gemma":0.0001058672,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004108163,"about_ca_topic_score_gemma":0.000002122849,"domain_scores_codex":[0.9967786,0.0002280366,0.0008003953,0.0005591837,0.0008943435,0.0007394578],"domain_scores_gemma":[0.9950796,0.00350616,0.000217788,0.0007911226,0.0001550164,0.0002503192],"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":[0.00005666935,0.0002769331,0.00005997351,0.000116559,0.00001051211,0.00001728792,0.01081877,0.00001945336,0.001465545,0.985485,0.00001718396,0.001656155],"study_design_scores_gemma":[0.0005421032,0.0003410734,0.0005047785,0.0002770381,0.00001458147,0.00001859996,0.0004311543,0.2274457,0.00139793,0.7687973,8.866469e-7,0.0002288819],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4754592,0.00001520551,0.5150352,0.0003039377,0.00008345704,0.000490848,0.00001475088,0.00004448067,0.008552914],"genre_scores_gemma":[0.7833632,0.000005305951,0.2164741,0.00008034856,0.0000397374,0.000008166044,0.000001545708,0.00001850707,0.000009151426],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.307904,"threshold_uncertainty_score":0.9999904,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02615349297190799,"score_gpt":0.3132956304514048,"score_spread":0.2871421374794968,"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."}}