{"id":"W2173879057","doi":"10.37236/5741","title":"A Hopf Algebraic Approach to Schur Function Identities","year":2017,"lang":"en","type":"preprint","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Hopf algebra; Schur's theorem; Mathematics; Pure mathematics; Algebraic number; Function (biology); Schur algebra; Algebra over a field; Mathematical analysis; Orthogonal polynomials","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":[0.001366336,0.000744596,0.0006777433,0.003055849,0.002080409,0.003713057,0.001203848,0.001000914,0.009705254],"category_scores_gemma":[0.003220459,0.0002812736,0.0007746484,0.002034646,0.003688501,0.006318369,0.002374907,0.00193915,0.001557607],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00161971,"about_ca_system_score_gemma":0.0009599184,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001026647,"about_ca_topic_score_gemma":0.0008323372,"domain_scores_codex":[0.9990063,0.0002637765,0.00005504685,0.0001533538,0.0003836879,0.000137841],"domain_scores_gemma":[0.9988948,0.0003476143,0.0001082752,0.0001687986,0.0003487249,0.0001317926],"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":[0.00000252033,0.000004305903,0.00003084655,0.000007639149,0.000001309608,0.00002095281,0.00004846571,0.0001860139,0.0001895968,0.9971415,0.0002481708,0.002118744],"study_design_scores_gemma":[0.000001854547,0.000005850426,0.000033569,0.000005370189,0.000002138103,0.00004371918,0.00002869343,0.002292654,0.0002860148,0.9951481,0.002147676,0.000004420127],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09663574,0.003729291,0.6198941,0.002888648,0.001480842,0.00009486877,0.0002399321,0.0002696248,0.2747669],"genre_scores_gemma":[0.8719661,0.003434386,0.06941233,0.00113137,0.002643831,0.0001212037,0.0002477607,0.0001589717,0.05088412],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009705254,"threshold_uncertainty_score":0.03246731,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04252571557234849,"score_gpt":0.3185492930964872,"score_spread":0.2760235775241388,"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."}}