{"id":"W2057158872","doi":"10.1016/j.jda.2012.04.015","title":"Cool-lex order and k-ary Catalan structures","year":2012,"lang":"en","type":"article","venue":"Journal of Discrete Algorithms","topic":"semigroups and automata theory","field":"Computer Science","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University; University of Victoria; University of Manitoba","funders":"","keywords":"Catalan number; Combinatorics; Lexicographical order; Mathematics; Complement (music); Order (exchange); Precomputation; Binary tree; Sequence (biology); Discrete mathematics; Algorithm; Computer science","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":[],"consensus_categories":[],"category_scores_codex":[0.0004608349,0.0001298205,0.0002110382,0.0001025084,0.00008272307,0.0001283107,0.0004986039,0.00005305821,0.00003709546],"category_scores_gemma":[0.00005529296,0.00008920331,0.00006559188,0.0001800621,0.00006182904,0.001176281,0.0001802679,0.0002023009,0.000005042396],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001783541,"about_ca_system_score_gemma":0.00004749183,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001267298,"about_ca_topic_score_gemma":5.669959e-7,"domain_scores_codex":[0.9989598,0.00005937862,0.0002902506,0.000113105,0.0002953983,0.0002820921],"domain_scores_gemma":[0.9990754,0.00007698145,0.000239524,0.0002353194,0.00008621712,0.0002865493],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"observational","study_design_scores_codex":[0.0001307175,0.0003327079,0.01500828,0.0001326583,0.0006469358,0.0003616027,0.01402614,0.0001094548,0.007398203,0.1504415,0.02624662,0.7851652],"study_design_scores_gemma":[0.0100456,0.00228288,0.5909029,0.0004978566,0.0003969978,0.01917175,0.003482374,0.07578347,0.02496564,0.1475618,0.1216397,0.003269046],"study_design_candidate":"design_other","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4995738,0.01678923,0.475959,0.002033303,0.003541441,0.0001841981,0.00002640768,0.0001158806,0.001776732],"genre_scores_gemma":[0.9158961,0.0001421201,0.08264777,0.0004639335,0.0007258674,7.539564e-7,0.000002003048,0.00001299439,0.0001084416],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7818962,"threshold_uncertainty_score":0.3637606,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009989566069584637,"score_gpt":0.2494760250303142,"score_spread":0.2394864589607295,"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."}}