{"id":"W2949488644","doi":"10.46298/dmtcs.3606","title":"Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables","year":2008,"lang":"en","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Invariant (physics); Mathematics; Algebra over a field; Pure mathematics; Mathematical physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001105489,0.000829637,0.0005699375,0.002468016,0.001601323,0.00281103,0.001242988,0.0006148386,0.006659493],"category_scores_gemma":[0.001230817,0.0002924574,0.001025985,0.001655655,0.004013687,0.003682305,0.001691385,0.001440274,0.001028622],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001202371,"about_ca_system_score_gemma":0.0009308147,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001365799,"about_ca_topic_score_gemma":0.001074455,"domain_scores_codex":[0.9992266,0.0001462517,0.00004379866,0.0001467393,0.0002215393,0.0002150989],"domain_scores_gemma":[0.9990232,0.0002313314,0.0002658534,0.00009335374,0.0001668183,0.0002195034],"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":[0.00001370956,0.00002119729,0.0002345293,0.00002072259,0.000005770717,0.00008480329,0.000298227,0.0007028587,0.0009866754,0.9949084,0.0001472947,0.002575827],"study_design_scores_gemma":[0.00001285224,0.00006052374,0.000491938,0.00001428948,0.0000129076,0.000153005,0.0002463644,0.01193561,0.002608623,0.9816876,0.002749465,0.00002689026],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7599528,0.001040842,0.1934911,0.0005253348,0.0003081154,0.00006980678,0.0002016692,0.0002084196,0.04420185],"genre_scores_gemma":[0.9738884,0.0005453308,0.01202143,0.00009995003,0.0002192791,0.00005522998,0.0001995303,0.00006249169,0.01290825],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006659493,"threshold_uncertainty_score":0.02227825,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02632181088456867,"score_gpt":0.2859250469567149,"score_spread":0.2596032360721462,"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."}}