{"id":"W2951948267","doi":"","title":"Non-crossing linked partitions, the partial order << on NC(n), and the S-transform","year":2009,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Bijection; Mathematics; Combinatorics; Free probability; Noncommutative geometry; Connection (principal bundle); Reciprocal; Order (exchange); Set (abstract data type); Cumulant; Discrete mathematics; Pure mathematics; Computer science; Statistics","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":[0.000892528,0.0004992319,0.0005665991,0.001579525,0.001186944,0.002376876,0.0007277841,0.0008120652,0.004880127],"category_scores_gemma":[0.003005317,0.0002373586,0.0004407004,0.001277822,0.003969622,0.003486548,0.001098275,0.001423248,0.0005095177],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001509881,"about_ca_system_score_gemma":0.0005403452,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008676032,"about_ca_topic_score_gemma":0.001112698,"domain_scores_codex":[0.999378,0.000162432,0.0000258528,0.0001138564,0.0002082556,0.0001115961],"domain_scores_gemma":[0.9984881,0.0007136198,0.0002930776,0.0001325269,0.0001647695,0.0002079853],"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":[0.00001459349,0.000005813509,0.0001015848,0.00001149762,0.000001431108,0.00004074265,0.00006247144,0.0004386046,0.0003870026,0.9966986,0.000349882,0.001887731],"study_design_scores_gemma":[0.000007161505,0.0000202059,0.0003501217,0.000009593797,0.000003079872,0.0001670652,0.00005214975,0.008920303,0.0005854065,0.9878106,0.002060359,0.00001391644],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6749618,0.003515481,0.2057278,0.002815232,0.0005926657,0.00004741152,0.0003313052,0.0002259714,0.1117824],"genre_scores_gemma":[0.9706081,0.0007237362,0.01568022,0.0002745908,0.0004632759,0.00004609765,0.000167063,0.00004996785,0.0119871],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004880127,"threshold_uncertainty_score":0.01632565,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0590739630772367,"score_gpt":0.3314725551292168,"score_spread":0.2723985920519801,"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."}}