{"id":"W2950575866","doi":"10.48550/arxiv.1112.4460","title":"The down operator and expansions of near rectangular k-Schur functions","year":2011,"lang":"en","type":"preprint","venue":"","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Operator (biology); Computer science; Mathematics","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":[0.0002370691,0.0003416316,0.0002378921,0.0008819279,0.0006188148,0.0008791877,0.0004293511,0.0002722068,0.006777142],"category_scores_gemma":[0.0009167468,0.0001448201,0.0002918121,0.0004152414,0.001207124,0.001747078,0.0009178148,0.001096079,0.0008041874],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003728557,"about_ca_system_score_gemma":0.0002631234,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004774707,"about_ca_topic_score_gemma":0.0004500759,"domain_scores_codex":[0.9998236,0.00003389829,0.000005716662,0.00003097326,0.00005699175,0.00004880228],"domain_scores_gemma":[0.9997258,0.00005932132,0.0000602786,0.00003303177,0.00005299779,0.00006856599],"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":[0.00003102881,0.00001570469,0.0003046781,0.00001828817,0.000002497031,0.0001902889,0.0002619738,0.00087002,0.006830418,0.9852646,0.0004150684,0.005795375],"study_design_scores_gemma":[0.00002522579,0.0000927948,0.001500967,0.00002481856,0.00001333757,0.0007473903,0.0006169794,0.0216606,0.01957563,0.9462125,0.009490093,0.00003965703],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8382763,0.0002657616,0.07605101,0.0003907669,0.0001038895,0.00003656797,0.00008959952,0.0001391113,0.08464691],"genre_scores_gemma":[0.973533,0.0002576902,0.009037679,0.0001133274,0.00008663274,0.00002486884,0.00005952631,0.00005773797,0.01682951],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006777142,"threshold_uncertainty_score":0.02267176,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0513257496784669,"score_gpt":0.3058545501001222,"score_spread":0.2545288004216553,"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."}}