{"id":"W1994928089","doi":"10.1016/s0012-365x(03)00094-3","title":"A permutation group determined by an ordered set","year":2003,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Advanced Algebra and Logic","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Permutation group; Combinatorics; Involution (esoterism); Symmetric group; Distributive lattice; Permutation (music); Primitive permutation group; Cyclic permutation; Finite group; Alternating group; Partial permutation; Discrete mathematics; Derangement; Group (periodic table); Lattice (music); Distributive property; Pure 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001675422,0.0001457551,0.0001556321,0.00003761845,0.0001086018,0.0001241326,0.0003932136,0.00004808906,0.00002882556],"category_scores_gemma":[0.00009306196,0.0001200968,0.00005479952,0.000201889,0.0000311955,0.0005308058,0.00004303333,0.00006993764,0.00004415548],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001861503,"about_ca_system_score_gemma":0.00001573654,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001199626,"about_ca_topic_score_gemma":0.000003090373,"domain_scores_codex":[0.9990298,0.0000604149,0.0002175414,0.0002612891,0.0001960012,0.0002349726],"domain_scores_gemma":[0.9992161,0.00006729872,0.0001039631,0.0004838024,0.00003322672,0.00009564624],"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":[0.000002622663,0.0001946183,0.00008323759,0.0000782775,0.00002041197,0.00002000013,0.006900673,0.00008973201,0.006081608,0.9796608,0.0004643304,0.006403666],"study_design_scores_gemma":[0.0008445875,0.000346669,0.00009400727,0.00003760697,0.00002553701,0.0001014575,0.001143687,0.242655,0.005341456,0.7451977,0.003522065,0.0006901895],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07447179,0.00005019772,0.9225575,0.00006047507,0.00007301671,0.0001519395,0.000005680499,0.0001583382,0.002470999],"genre_scores_gemma":[0.76344,0.000004361132,0.2360772,0.0001678524,0.00001186385,0.00002118253,0.00002333304,0.00001431203,0.0002398374],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.6889682,"threshold_uncertainty_score":0.4897405,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01925120806903717,"score_gpt":0.27033289119288,"score_spread":0.2510816831238428,"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."}}