{"id":"W1537254652","doi":"10.1016/j.jcta.2017.05.003","title":"Multiplicative structures of the immaculate basis of non-commutative symmetric functions","year":2017,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series A","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada","keywords":"Basis (linear algebra); Mathematics; Commutative property; Multiplicative function; Symmetric function; Complete homogeneous symmetric polynomial; Commutative algebra; Pure mathematics; Polytope; Commutative ring; Ring of symmetric functions; Algebra over a field; Discrete mathematics; Geometry; Mathematical analysis","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":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.001136124,0.0002675276,0.0009453149,0.0001840226,0.0004470466,0.00004815348,0.001470157,0.0001450312,0.00004356283],"category_scores_gemma":[0.009030143,0.0001754381,0.0004883094,0.0003249208,0.0007424568,0.0005273451,0.0003952043,0.0004918788,9.712628e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009661294,"about_ca_system_score_gemma":0.0001722992,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007885019,"about_ca_topic_score_gemma":0.000001411689,"domain_scores_codex":[0.9974484,0.0003543543,0.001182554,0.0001390913,0.0006568531,0.0002187111],"domain_scores_gemma":[0.9901358,0.002107725,0.005164896,0.001186624,0.001317807,0.00008715272],"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":[0.0007899762,0.0002907033,0.0002680918,0.0001465936,0.0004413819,0.000004213334,0.002084106,0.00002248409,0.003588844,0.9915093,0.0001629709,0.0006913117],"study_design_scores_gemma":[0.001934932,0.0004806818,0.00123291,0.0002127257,0.000267745,0.0000422863,0.001406638,0.00001763697,0.07368598,0.9203872,0.0001845002,0.00014674],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9755202,0.0001559293,0.006923935,0.0003363499,0.01028082,0.000757366,0.00006007284,0.00001968355,0.005945658],"genre_scores_gemma":[0.9937383,0.00002515145,0.00569967,0.000004972964,0.0002631149,0.000007438483,3.150189e-7,0.00003988449,0.0002211439],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0711221,"threshold_uncertainty_score":0.9993172,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02521448372140004,"score_gpt":0.321784094441272,"score_spread":0.296569610719872,"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."}}