{"id":"W79648173","doi":"","title":"On Generalizing Motzkin Numbers using k-Trees.","year":2008,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Topological and Geometric Data Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Combinatorics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001592894,0.0001458131,0.0002112547,0.0002201453,0.0002868652,0.00006492206,0.0008480262,0.00006951218,0.00006168804],"category_scores_gemma":[0.0001118599,0.0001222474,0.0001110015,0.001587702,0.00006667451,0.0003178656,0.0002714741,0.0001407052,0.0001670488],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000645306,"about_ca_system_score_gemma":0.00003187197,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003483234,"about_ca_topic_score_gemma":0.000004027073,"domain_scores_codex":[0.9986349,0.00006769122,0.0002008911,0.0004123485,0.0003604109,0.0003236987],"domain_scores_gemma":[0.9990007,0.0001186438,0.00008144905,0.0006173477,0.00004972781,0.0001320803],"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":[0.00000275132,0.0001363267,0.003722815,0.000001420695,0.00003336754,0.0001961573,0.0001018767,0.0006242679,0.0001658918,0.9886734,0.004494599,0.001847127],"study_design_scores_gemma":[0.001401442,0.0002942574,0.01511485,0.00002227955,0.00003739679,0.000181154,0.00002556373,0.05964654,0.001843146,0.9116107,0.008975856,0.0008468736],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9839056,0.0001110041,0.01143201,0.000303917,0.00104857,0.00005585067,0.000002746764,0.0001614513,0.002978863],"genre_scores_gemma":[0.9926175,0.00002787443,0.006538704,0.0004867918,0.00001076336,0.0000025379,0.000004249334,0.00000640534,0.0003052012],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07706275,"threshold_uncertainty_score":0.4985103,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0356430785303864,"score_gpt":0.2574134179686212,"score_spread":0.2217703394382348,"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."}}