{"id":"W2511042131","doi":"10.1007/s00233-017-9867-4","title":"The Frobenius problem for the shuffle operation","year":2017,"lang":"en","type":"preprint","venue":"Semigroup Forum","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Winnipeg","funders":"","keywords":"Iterated function; Word (group theory); Computer science; Finite set; Mathematics; Combinatorics; Discrete mathematics; Theoretical computer science; Geometry","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":[0.002205615,0.0006211998,0.001330418,0.001413862,0.002387977,0.003836815,0.001236274,0.00291951,0.01028804],"category_scores_gemma":[0.007172663,0.0005656748,0.001005254,0.001157442,0.005055684,0.01325321,0.002596705,0.004124184,0.001799809],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001627464,"about_ca_system_score_gemma":0.001566074,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009999631,"about_ca_topic_score_gemma":0.0006227327,"domain_scores_codex":[0.9988282,0.0003252173,0.00006381802,0.000305774,0.0002411547,0.0002358318],"domain_scores_gemma":[0.996956,0.001927076,0.0002067201,0.0003963225,0.0002387635,0.0002752342],"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":[0.00004202324,0.00001448652,0.00007314738,0.00002821482,0.000003758365,0.00003199366,0.0001236961,0.001060525,0.0003965307,0.993501,0.0009992544,0.003725412],"study_design_scores_gemma":[0.000006484202,0.000004440224,0.00003103197,0.000004560671,0.00000136685,0.00002297955,0.00002511986,0.002627573,0.0002432272,0.9962634,0.0007626147,0.000007238426],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4471558,0.002368769,0.4532144,0.01277048,0.0008926847,0.00008173752,0.0005955734,0.0003473359,0.08257321],"genre_scores_gemma":[0.9233008,0.001232236,0.0321638,0.0005817994,0.001077532,0.0001330422,0.0003817461,0.0002356031,0.04089338],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01028804,"threshold_uncertainty_score":0.03441691,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01783093246505464,"score_gpt":0.2706545985434372,"score_spread":0.2528236660783826,"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."}}