{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002942001,0.0006151842,0.000871001,0.0003603368,0.0002309533,0.0001098374,0.0004923737,0.000596869,0.0002348686],"category_scores_gemma":[0.001208585,0.0005962582,0.0002027311,0.0005109319,0.0001252524,0.0001525925,0.0007951502,0.001172032,0.0003341064],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001958459,"about_ca_system_score_gemma":0.0001443304,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003003682,"about_ca_topic_score_gemma":0.00001090756,"domain_scores_codex":[0.9973519,0.0001238802,0.0007859124,0.0008103605,0.0004266617,0.0005012246],"domain_scores_gemma":[0.9971087,0.0007098306,0.0003625326,0.001407356,0.0001763319,0.0002352415],"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":[0.0002383644,0.004827236,0.104562,0.009022749,0.002665009,0.0003756413,0.006353342,0.0005019424,0.0008245843,0.8353043,0.02023866,0.01508613],"study_design_scores_gemma":[0.001098153,0.0001587975,0.003379463,0.0005993265,0.0005509605,0.0000573246,0.0002700258,0.0003220195,0.000739756,0.9863005,0.005308979,0.001214641],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9799536,0.0007624464,0.002609982,0.000258752,0.002082843,0.0008952178,0.00005345241,0.0004799154,0.01290373],"genre_scores_gemma":[0.9872351,0.0003688733,0.00799785,0.00007111122,0.0005691282,0.0001934828,0.00003302653,0.0001770948,0.003354324],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1509962,"threshold_uncertainty_score":0.9996489,"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."}}