{"id":"W2597540427","doi":"10.46298/dmtcs.2894","title":"The Murnaghan―Nakayama rule for k-Schur functions","year":2011,"lang":"fr","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Drexel University; National Science Foundation","keywords":"Mathematics; Schur's theorem; Noncommutative geometry; Schur algebra; Symmetric function; Schur polynomial; Affine transformation; Schur complement; Schur's lemma; Pure mathematics; Combinatorics; Algebra over a field; Macdonald polynomials; Eigenvalues and eigenvectors; Orthogonal polynomials; Physics","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":[0.001279597,0.0004825587,0.0005012151,0.001126475,0.00116343,0.001395649,0.0009188771,0.0005873395,0.004813664],"category_scores_gemma":[0.002713781,0.000265042,0.001132821,0.0006612039,0.002390044,0.002879383,0.001373897,0.002093579,0.00170543],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000626636,"about_ca_system_score_gemma":0.0006367966,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001085886,"about_ca_topic_score_gemma":0.001360399,"domain_scores_codex":[0.9993057,0.0001226311,0.00004172349,0.0001156765,0.0003037274,0.0001104629],"domain_scores_gemma":[0.9991857,0.0002666841,0.00008245825,0.0001176087,0.0002779717,0.000069525],"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":[0.00001671886,0.00001096577,0.0002859976,0.00004850514,0.000006747923,0.000274761,0.0004731697,0.0005838565,0.003158459,0.981052,0.0009551183,0.01313365],"study_design_scores_gemma":[0.00001574183,0.00007350723,0.0008170712,0.00004126596,0.0000211918,0.0008138291,0.0001845703,0.008748853,0.01058639,0.9556263,0.02302174,0.00004954254],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2349275,0.001837908,0.6093274,0.001915577,0.001186086,0.0001298852,0.0002009422,0.0003367264,0.150138],"genre_scores_gemma":[0.8185477,0.001495623,0.1357284,0.0008232114,0.0006684242,0.0001884333,0.0001099465,0.000260509,0.04217771],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004813664,"threshold_uncertainty_score":0.01610333,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03228027561604391,"score_gpt":0.2892858517904384,"score_spread":0.2570055761743945,"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."}}