{"id":"W2342581660","doi":"10.4169/math.mag.89.1.16","title":"Transposition as a Permutation: A Tale of Group Actions and Modular Arithmetic","year":2016,"lang":"en","type":"article","venue":"Mathematics Magazine","topic":"Cellular Automata and Applications","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Acadia University","funders":"","keywords":"Mathematics; Permutation matrix; Combinatorics; Multiplicative group; Permutation group; Group (periodic table); Multiplicative function; Arithmetic; Chinese remainder theorem; Modulo; Permutation (music); Transposition (logic); Symmetric group; Cyclic permutation; Matrix (chemical analysis); Prime (order theory); Discrete mathematics","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":[0.001388031,0.0003073792,0.0002600706,0.0008974556,0.001895956,0.00350246,0.0005626158,0.0009958622,0.005887418],"category_scores_gemma":[0.002652348,0.000212389,0.00047103,0.0006280402,0.008759747,0.007186803,0.001662246,0.002421672,0.0009613654],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001515837,"about_ca_system_score_gemma":0.0007249242,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001494529,"about_ca_topic_score_gemma":0.001568358,"domain_scores_codex":[0.9994715,0.0002533783,0.00002244505,0.00007267536,0.0001223584,0.00005767574],"domain_scores_gemma":[0.9992969,0.0003442018,0.00003803635,0.0001574631,0.00009107641,0.00007227406],"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":[0.000006680914,0.000004100934,0.00003397566,0.000006930739,0.000001903659,0.00002856441,0.000294594,0.0004133599,0.0001480603,0.9915759,0.002563356,0.004922464],"study_design_scores_gemma":[0.000003814395,0.000005719721,0.00003545214,0.000008695953,0.000001206192,0.00002243117,0.00009396906,0.001011644,0.0001153798,0.9814141,0.01728288,0.000004685659],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.08146266,0.01732377,0.217662,0.1071623,0.005173287,0.00008306283,0.0001886429,0.0008538053,0.5700905],"genre_scores_gemma":[0.8420563,0.007532977,0.06943078,0.005679028,0.002636676,0.0001250639,0.00009411911,0.0003336965,0.07211129],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005887418,"threshold_uncertainty_score":0.0196954,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01284889694325481,"score_gpt":0.239304930961297,"score_spread":0.2264560340180422,"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."}}