{"id":"W2149963403","doi":"10.1017/s0004972713000208","title":"ON PERMUTATION BINOMIALS OVER FINITE FIELDS","year":2013,"lang":"en","type":"article","venue":"Bulletin of the Australian Mathematical Society","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"Brock University","funders":"","keywords":"Finite field; Binomial (polynomial); Gaussian binomial coefficient; Permutation (music); Partial permutation; Binomial coefficient; Cyclic permutation; Generalized permutation matrix; Divisor (algebraic 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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0003273868,0.0001138845,0.0001516797,0.00001371385,0.0001094903,0.00008372807,0.0007549356,0.00009605086,0.002830412],"category_scores_gemma":[0.0001485936,0.00007356977,0.0003706184,0.0001551841,0.0001195975,0.00004353826,0.0001587299,0.0001578479,0.0004793336],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001278741,"about_ca_system_score_gemma":0.000009527165,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001199367,"about_ca_topic_score_gemma":6.95813e-8,"domain_scores_codex":[0.9990605,0.00008207448,0.0002400321,0.0001804644,0.000245678,0.000191233],"domain_scores_gemma":[0.9986982,0.0005650494,0.0001119154,0.0005290126,0.00003915816,0.00005668623],"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":[0.000003325761,0.0001665793,0.00008648125,0.00008980232,0.00004525082,2.590333e-7,0.00127047,0.000159324,0.0005401847,0.7588515,0.2375595,0.001227347],"study_design_scores_gemma":[0.0003394015,0.0001130784,0.004058458,0.0001406049,0.00001999061,0.000003248559,0.000106905,0.003164422,0.004202613,0.9802467,0.007385202,0.0002194248],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.730898,0.00001120777,0.1863151,0.06627392,0.0004446562,0.0009961162,0.000007653607,0.0002413648,0.01481196],"genre_scores_gemma":[0.9788135,0.000001276069,0.01622331,0.001473125,0.00003134148,0.00002307857,3.719235e-7,0.000006543748,0.003427439],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2479155,"threshold_uncertainty_score":0.9980811,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01706719996674736,"score_gpt":0.2392756072454778,"score_spread":0.2222084072787304,"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."}}