{"id":"W4411497698","doi":"10.1017/mag.2025.10084","title":"109.18 Transitivity, transpositions and permutation groups","year":2025,"lang":"en","type":"article","venue":"The Mathematical Gazette","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of New Brunswick","funders":"","keywords":"Transitive relation; Permutation (music); Permutation group; Combinatorics; Mathematics; Physics","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":[0.0004241994,0.0003091434,0.0002637908,0.0008551531,0.00143582,0.002165322,0.0002584319,0.0005618613,0.0536273],"category_scores_gemma":[0.0009694194,0.0001792451,0.0005741688,0.0009767072,0.002345137,0.002633563,0.001048696,0.001429411,0.008023204],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001470215,"about_ca_system_score_gemma":0.0005821826,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001721207,"about_ca_topic_score_gemma":0.001548979,"domain_scores_codex":[0.9996581,0.0001151991,0.00001687952,0.00007963624,0.00007906571,0.0000511197],"domain_scores_gemma":[0.9997354,0.00008480452,0.0000288996,0.00005965838,0.00005800255,0.00003319093],"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":[0.00001449213,0.000005004781,0.0000781676,0.00002152029,0.000002660535,0.00002871131,0.0001834193,0.00007852999,0.0003483144,0.9850677,0.008063345,0.006108251],"study_design_scores_gemma":[0.0000109175,0.00002360313,0.0003985023,0.00003369465,0.000008060845,0.0001919383,0.0001748667,0.0001998379,0.0005324371,0.9095216,0.08889776,0.000006784702],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.02210185,0.002703871,0.01780471,0.004144765,0.0008819056,0.00002486821,0.0006462209,0.000165871,0.9515258],"genre_scores_gemma":[0.5693653,0.003504388,0.01312707,0.001717923,0.001334206,0.00008945019,0.001326498,0.0003542172,0.409181],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0536273,"threshold_uncertainty_score":0.1794012,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06114139082458708,"score_gpt":0.3616486660610184,"score_spread":0.3005072752364313,"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."}}