{"id":"W2146949677","doi":"10.1006/eujc.2000.0409","title":"Transitive Factorizations in the Symmetric Group, and Combinatorial Aspects of Singularity Theory","year":2000,"lang":"en","type":"article","venue":"European Journal of Combinatorics","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":18,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Monodromy; Symmetric group; Combinatorics; Conjecture; Alternating group; Group (periodic table); Permutation group; Permutation (music); Combinatorial proof; Generating function; Series (stratigraphy); Holomorphic function; Partition (number theory); Pure mathematics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008987157,0.000544412,0.0007467879,0.001900129,0.002398964,0.004072241,0.000800447,0.001257454,0.004447628],"category_scores_gemma":[0.003585921,0.0004373063,0.0007634014,0.001477256,0.005181406,0.007163654,0.001793095,0.001709365,0.0004436177],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001280022,"about_ca_system_score_gemma":0.0008225607,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001341957,"about_ca_topic_score_gemma":0.001462724,"domain_scores_codex":[0.9993731,0.0001655891,0.00004600683,0.0001148866,0.0001912655,0.0001092147],"domain_scores_gemma":[0.9984643,0.0006479696,0.0003285157,0.0001900206,0.0001459689,0.0002232887],"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":[0.00001453908,0.00001002967,0.0001229267,0.00001282127,0.000002249971,0.00004395021,0.000154678,0.0004429667,0.0002179673,0.9969962,0.0004138633,0.001567838],"study_design_scores_gemma":[0.000006223469,0.000006881168,0.00006418492,0.000004158292,0.000001996952,0.0000565876,0.00006405699,0.001000882,0.00005186192,0.9980198,0.0007195181,0.000003723887],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7326434,0.004465487,0.1123961,0.006182958,0.0005660449,0.00008622724,0.0003639742,0.0001511019,0.1431447],"genre_scores_gemma":[0.978556,0.00107511,0.009335994,0.0002463987,0.0005465686,0.00003145066,0.0001436066,0.00002515285,0.01003968],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004447628,"threshold_uncertainty_score":0.01487881,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01029537145746291,"score_gpt":0.207856369470658,"score_spread":0.1975609980131951,"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."}}