{"id":"W2123948060","doi":"10.1007/s00026-013-0177-6","title":"Multiplicity Free Schur, Skew Schur, and Quasisymmetric Schur Functions","year":2013,"lang":"en","type":"article","venue":"Annals of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Multiplicity (mathematics); Schur's theorem; Schur's lemma; Schur polynomial; Combinatorics; Skew; Schur algebra; Schur product theorem; Schur complement; Schur decomposition; Discrete mathematics; Pure mathematics; Macdonald polynomials; Orthogonal polynomials; Mathematical analysis; Computer science; Discrete orthogonal polynomials; Gegenbauer polynomials; Classical 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":[0.001334247,0.001094352,0.0008931746,0.003084577,0.002311814,0.003461122,0.001073029,0.001085034,0.008251824],"category_scores_gemma":[0.00481903,0.0004448559,0.0009357,0.001703674,0.003939593,0.005586782,0.00213513,0.002242418,0.001006835],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0015688,"about_ca_system_score_gemma":0.00095595,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00150318,"about_ca_topic_score_gemma":0.001624563,"domain_scores_codex":[0.9993469,0.000154403,0.00003453814,0.0001009346,0.0002172123,0.0001460601],"domain_scores_gemma":[0.997716,0.0008842215,0.0003669231,0.0002770764,0.0003337096,0.000422158],"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":[0.00003861521,0.00001207301,0.0002130198,0.00001230918,0.000003398409,0.00006315558,0.0001136884,0.0004131096,0.0003865033,0.9941608,0.0006937098,0.003889484],"study_design_scores_gemma":[0.00001056152,0.00001410791,0.0001996845,0.000006418151,0.000006896343,0.000146697,0.0000557821,0.002862943,0.0003584097,0.9949397,0.001384017,0.00001476325],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7237487,0.002571687,0.1474262,0.002837254,0.0006669271,0.00006851993,0.0004569828,0.0002796078,0.1219442],"genre_scores_gemma":[0.9688657,0.0007639921,0.006906917,0.0002549694,0.0007115514,0.00004350773,0.0001914439,0.00005855058,0.02220332],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008251824,"threshold_uncertainty_score":0.02760506,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09868087161366132,"score_gpt":0.3444571678942561,"score_spread":0.2457762962805948,"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."}}