{"id":"W2963188278","doi":"10.1090/tran/7143","title":"Contents of partitions and the combinatorics of permutation factorizations in genus $0$","year":2016,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Combinatorics; Permutation (music); Genus; Enumerative combinatorics; Permutation group; Discrete mathematics; Botany; Biology","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0003740885,0.0001355296,0.0005626418,0.00003357453,0.00008821709,0.000004295064,0.0002766937,0.0000464993,0.0000281631],"category_scores_gemma":[0.0007488873,0.00006925751,0.0002914211,0.0005473604,0.001718099,0.0000929425,0.00002900454,0.0001220689,8.535566e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005383163,"about_ca_system_score_gemma":0.00003457003,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002487759,"about_ca_topic_score_gemma":0.000004599744,"domain_scores_codex":[0.9984966,0.0001504612,0.000731395,0.0001243254,0.0003417476,0.0001555031],"domain_scores_gemma":[0.9956431,0.002983883,0.0006891554,0.0004581199,0.0001876919,0.00003805635],"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":[0.00005355734,0.0007764037,0.0005713481,0.0004287691,0.0001690931,8.16535e-8,0.005372939,0.00004843076,0.005089055,0.9866389,0.00003611442,0.00081531],"study_design_scores_gemma":[0.001509775,0.00006667371,0.0007304716,0.0002160998,0.0001624816,0.00000312222,0.001826769,0.0006276416,0.006854507,0.9879064,0.000007165534,0.00008890658],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5555704,0.00001991025,0.4426922,0.00079218,0.00007231798,0.0005394449,0.00005243335,0.00001997573,0.0002411153],"genre_scores_gemma":[0.9902014,0.00007357197,0.009554681,0.00001151078,0.000005511057,0.00004850544,2.786603e-7,0.00001876959,0.00008583197],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4346309,"threshold_uncertainty_score":0.6330409,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02663272084212012,"score_gpt":0.2919409959109921,"score_spread":0.265308275068872,"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."}}