{"id":"W1992204596","doi":"10.1007/s10801-006-0020-9","title":"Classical symmetric functions in superspace","year":2006,"lang":"en","type":"article","venue":"Journal of Algebraic Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université Laval","funders":"Fondo Nacional de Desarrollo Científico y Tecnológico; Natural Sciences and Engineering Research Council of Canada","keywords":"Symmetric function; Ring of symmetric functions; Superspace; Multiplicative function; Symmetric closure; Symmetric group; Complete homogeneous symmetric polynomial; Symmetric space; Invariant (physics); Triple system","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":[],"consensus_categories":[],"category_scores_codex":[0.0007255512,0.0002639469,0.0006819239,0.0008053911,0.00008357039,0.00005509222,0.0004299293,0.0001912525,0.00003846775],"category_scores_gemma":[0.002232917,0.0002387392,0.0002552506,0.00196288,0.0000722898,0.0003535569,0.00009268834,0.0007823944,0.00002228668],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005732555,"about_ca_system_score_gemma":0.0001874254,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000075003,"about_ca_topic_score_gemma":0.00001048914,"domain_scores_codex":[0.9972696,0.0001290526,0.001169168,0.0001888408,0.000830762,0.000412548],"domain_scores_gemma":[0.9966229,0.001658078,0.0007247831,0.000376424,0.0004711272,0.000146698],"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":[0.00002832037,0.001192263,0.001417567,0.00006375342,0.00002820527,0.0001463557,0.0001083254,0.00002587177,0.0001511446,0.9869581,0.009684254,0.0001958518],"study_design_scores_gemma":[0.002032185,0.0003177886,0.0009291684,0.00009413555,0.00006985036,0.0002532659,0.0002982653,0.0001508423,0.000261055,0.9915375,0.003816868,0.0002391231],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9661698,0.0007941304,0.01481669,0.002086511,0.004415859,0.0003530843,0.000003246507,0.00009855189,0.01126218],"genre_scores_gemma":[0.9931602,0.00002147292,0.004969661,0.00001824784,0.0003386236,0.00000551337,7.560709e-7,0.00005547489,0.001430007],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02699049,"threshold_uncertainty_score":0.9735503,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02060072849965508,"score_gpt":0.2813561582718396,"score_spread":0.2607554297721845,"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."}}