{"id":"W1927422331","doi":"10.1007/s00026-016-0321-1","title":"A Generating Tree Approach to k-Nonnesting Partitions and Permutations","year":2016,"lang":"en","type":"article","venue":"Annals of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"Capilano University; Simon Fraser University","funders":"","keywords":"Mathematics; Enumeration; Combinatorics; Permutation (music); Partition (number theory); Bounded function; Discrete mathematics; Tree (set theory); Generating function; Young tableau; Lattice (music)","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":[0.0004183462,0.000182543,0.0003400968,0.000130363,0.0001656499,0.00002650098,0.0001870777,0.00007515577,0.000005234297],"category_scores_gemma":[0.003301843,0.0001429957,0.00006771497,0.0004015151,0.00006930724,0.0001982284,0.0001208172,0.00008986121,0.000007404112],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002230846,"about_ca_system_score_gemma":0.00004453468,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002355833,"about_ca_topic_score_gemma":0.00000138152,"domain_scores_codex":[0.9985809,0.00006852005,0.0004965898,0.000248338,0.0003014915,0.0003041571],"domain_scores_gemma":[0.9976667,0.001111388,0.0002368241,0.0003870834,0.0004240167,0.0001740594],"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":[0.00000442411,0.0002892572,0.0001579414,0.0001035593,0.00002313652,0.000001182637,0.0007467192,0.00002431542,0.001977556,0.9938333,0.001245021,0.001593599],"study_design_scores_gemma":[0.000407347,0.0001237854,0.00009750105,0.0001344653,0.00002503962,0.00001009208,0.0001999388,0.0004269222,0.004963837,0.9930396,0.0003664361,0.0002050275],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7204297,0.000113423,0.2650001,0.001755661,0.0003109171,0.0005606934,0.00002170238,0.000189699,0.01161807],"genre_scores_gemma":[0.955568,0.00002465238,0.04380128,0.00008559509,0.00006088888,0.00007717097,0.000001351786,0.00003934799,0.0003417248],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2351383,"threshold_uncertainty_score":0.5831197,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.153119084515007,"score_gpt":0.3703183694863432,"score_spread":0.2171992849713362,"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."}}