{"id":"W2950764400","doi":"10.48550/arxiv.math/0008163","title":"Ribbon Operators and Hall-Littlewood Symmetric Functions","year":2000,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Ribbon; Combinatorics; Symmetric function; Operator (biology); Permutation (music); Mathematics; Function (biology); Partition function (quantum field theory); Partition (number theory); Physics; Geometry; Quantum mechanics","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":[0.0004854699,0.0004087412,0.0003264426,0.001063771,0.0008163,0.001230746,0.000552578,0.0005815147,0.007744569],"category_scores_gemma":[0.001099188,0.0001725295,0.0004303115,0.0007858966,0.001902336,0.001841535,0.000968997,0.0007801968,0.001043337],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007050061,"about_ca_system_score_gemma":0.0003444124,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004760541,"about_ca_topic_score_gemma":0.000631799,"domain_scores_codex":[0.9996896,0.00009317996,0.00001163004,0.0000446585,0.00007260227,0.00008839795],"domain_scores_gemma":[0.9994696,0.000155954,0.0000997524,0.00006224743,0.00005919639,0.0001532551],"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":[0.00001903949,0.000008783421,0.00005638224,0.000009381647,0.000001167397,0.00003439829,0.00009150256,0.0004007912,0.001017776,0.9948258,0.0004980229,0.003036897],"study_design_scores_gemma":[0.00001000137,0.00001976292,0.0002515647,0.000006268176,0.000002749849,0.00007896051,0.00008508519,0.006508807,0.001330322,0.9888363,0.002860054,0.00001006458],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6127235,0.001125186,0.1998613,0.0009152867,0.0003128096,0.00005550062,0.0002208704,0.0005086655,0.1842769],"genre_scores_gemma":[0.9501044,0.0004512663,0.02660187,0.0002579269,0.000189086,0.00005646284,0.0001002909,0.0001067481,0.02213192],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007744569,"threshold_uncertainty_score":0.02590823,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07620595273023352,"score_gpt":0.3176938220125017,"score_spread":0.2414878692822682,"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."}}