{"id":"W2525505959","doi":"10.46298/dmtcs.2744","title":"Refinements of the Littlewood-Richardson rule","year":2009,"lang":"fr","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Okanagan University College; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Schur polynomial; Product (mathematics); Pure mathematics; Combinatorics; Macdonald polynomials; Geometry","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":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.003078073,0.0007562472,0.001169327,0.0002122214,0.0006778151,0.0003241306,0.003985276,0.0002893268,0.00041087],"category_scores_gemma":[0.002397557,0.0005395098,0.0005134271,0.002229531,0.006492492,0.000526557,0.001532616,0.0007644694,0.0001297402],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002579848,"about_ca_system_score_gemma":0.0003248015,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002493878,"about_ca_topic_score_gemma":5.41877e-7,"domain_scores_codex":[0.9929353,0.0002825414,0.001816805,0.0009117234,0.002652647,0.00140099],"domain_scores_gemma":[0.993495,0.001297425,0.001085503,0.002919896,0.0007517225,0.0004503823],"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":[0.00001237238,0.001062234,0.000009335941,0.0006409303,0.00003926885,0.000006880929,0.00329311,0.00004951614,0.001366198,0.9868018,0.0003577988,0.006360522],"study_design_scores_gemma":[0.0005812812,0.0004329969,0.00007200892,0.001733342,0.0002140257,0.00005687719,0.000179945,0.08369625,0.01097896,0.9012291,0.0002820931,0.0005430882],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07656301,0.0007382203,0.8681394,0.008745134,0.006508491,0.002006699,0.00008569249,0.0002299002,0.03698347],"genre_scores_gemma":[0.5936781,0.00003787478,0.4048689,0.0003144802,0.0003669018,0.00001335121,0.000001576183,0.00006414451,0.0006546567],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.5171151,"threshold_uncertainty_score":0.9997057,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01616321636509368,"score_gpt":0.2912737679531027,"score_spread":0.275110551588009,"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."}}