{"id":"W2963648299","doi":"10.4064/aa148-2-2","title":"On the index of sequences over cyclic groups","year":2011,"lang":"en","type":"article","venue":"Acta Arithmetica","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":21,"is_retracted":false,"has_abstract":true,"ca_institutions":"Brock University","funders":"National Natural Science Foundation of China","keywords":"Mathematics; Combinatorics; Subsequence; Multiplicity (mathematics); Conjecture; Prime (order theory); Cyclic group; Sequence (biology); Order (exchange); Finite group; Group (periodic table); Geometry; Physics; Mathematical analysis; Bounded function","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":[0.001722231,0.0006325521,0.0009322002,0.002883498,0.001685908,0.002589153,0.001110932,0.000988392,0.004035484],"category_scores_gemma":[0.01078996,0.0003967941,0.0004720658,0.001897406,0.003472683,0.006217655,0.002411234,0.002122457,0.001132397],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001721325,"about_ca_system_score_gemma":0.0007021838,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005792977,"about_ca_topic_score_gemma":0.0003589792,"domain_scores_codex":[0.9984874,0.0003057414,0.0001151086,0.0002796878,0.0004921083,0.0003200169],"domain_scores_gemma":[0.9938533,0.003305168,0.0009196344,0.0005941885,0.0006824958,0.0006451882],"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":[0.0005416357,0.00009366689,0.00389656,0.0001760257,0.00002061468,0.0004639764,0.00160654,0.003153286,0.009116821,0.9444225,0.003132917,0.03337556],"study_design_scores_gemma":[0.00005382446,0.0001787447,0.002439186,0.0001436882,0.00002544467,0.0007003971,0.0003055383,0.01425416,0.007387371,0.9549932,0.01946773,0.00005065945],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7189453,0.00596649,0.0981663,0.002492465,0.0008956334,0.00009262657,0.0005583192,0.0003915923,0.1724912],"genre_scores_gemma":[0.9540534,0.002406574,0.02735842,0.0004351733,0.001130452,0.0001261124,0.000569446,0.0001888375,0.01373144],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004035484,"threshold_uncertainty_score":0.01349998,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1268940578476488,"score_gpt":0.330255429576126,"score_spread":0.2033613717284772,"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."}}