{"id":"W2740627096","doi":"10.1016/j.aam.2017.11.006","title":"A minimaj-preserving crystal on ordered multiset partitions","year":2017,"lang":"en","type":"article","venue":"Advances in Applied Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"Simons Foundation; National Science Foundation","keywords":"Multiset; Generalization; Conjecture; Statistic; Property (philosophy); Partition (number theory); Crystal (programming language)","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":[0.0005387205,0.000446793,0.001209961,0.001818997,0.004372847,0.00397858,0.00121536,0.00150656,0.009829999],"category_scores_gemma":[0.00160878,0.0007105201,0.001164792,0.001353634,0.002474321,0.003547501,0.002456486,0.002961935,0.001181042],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001060164,"about_ca_system_score_gemma":0.0009152265,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001116918,"about_ca_topic_score_gemma":0.001705873,"domain_scores_codex":[0.9993716,0.00009348235,0.00003292615,0.0001278601,0.0002191089,0.0001551433],"domain_scores_gemma":[0.9990319,0.0002550168,0.0001088826,0.0001528024,0.0001994986,0.0002519585],"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":[0.00004430228,0.00001741729,0.0000841909,0.00002217619,0.000004887966,0.00005383871,0.00009321597,0.0005103454,0.001651054,0.993821,0.001242777,0.002454866],"study_design_scores_gemma":[0.00002281524,0.00002404788,0.0001746618,0.00001281506,0.000005617562,0.0001660835,0.0001171943,0.00513311,0.001045559,0.989861,0.003420179,0.00001692748],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5592496,0.0008300603,0.2193652,0.002297983,0.001623246,0.0001376989,0.0009595071,0.0005941314,0.2149427],"genre_scores_gemma":[0.8570706,0.0004703528,0.06310555,0.0006870503,0.000493852,0.0001683432,0.0007443748,0.000730664,0.07652922],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009829999,"threshold_uncertainty_score":0.0328846,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05356525700061415,"score_gpt":0.3713117681047803,"score_spread":0.3177465111041661,"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."}}