{"id":"W2407803650","doi":"","title":"On bounds for the norms of circulant matrices with the generalized Fibonacci and Lucas numbers.","year":2011,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Fibonacci number; Circulant matrix; Lucas number; Mathematics; Fibonacci polynomials; Lucas sequence; Pisano period; Combinatorics; Algebra over a field; Pure mathematics; Discrete mathematics; Arithmetic; Orthogonal polynomials; Classical orthogonal polynomials","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00842509,0.004595355,0.002789136,0.008012369,0.003430828,0.00852288,0.00656942,0.004042228,0.01786738],"category_scores_gemma":[0.06571478,0.001642268,0.001888905,0.005922371,0.0078349,0.01719291,0.00868615,0.0117786,0.005961512],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004661737,"about_ca_system_score_gemma":0.002536031,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003294983,"about_ca_topic_score_gemma":0.006655974,"domain_scores_codex":[0.9941021,0.001762695,0.0002569583,0.0007361674,0.00224933,0.0008927867],"domain_scores_gemma":[0.9415582,0.04417154,0.002872428,0.00292867,0.005281546,0.003187582],"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":[0.0001441476,0.00008033603,0.0007277478,0.0002788448,0.00004821479,0.0001349473,0.0004504224,0.006751193,0.001338148,0.9586482,0.0112905,0.02010726],"study_design_scores_gemma":[0.00001607469,0.00004455277,0.0005619768,0.0001983772,0.00003644071,0.0001911893,0.000150385,0.02943187,0.0009287145,0.9586952,0.009686379,0.00005885471],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07077368,0.03859458,0.5957105,0.01126126,0.004019239,0.0002580437,0.002024008,0.001416118,0.2759426],"genre_scores_gemma":[0.6347281,0.01942462,0.2798392,0.004223984,0.007752879,0.001544624,0.002593427,0.001904783,0.04798845],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01786738,"threshold_uncertainty_score":0.05977237,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01423402091550357,"score_gpt":0.2474128530370896,"score_spread":0.233178832121586,"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."}}