{"id":"W2149698442","doi":"10.37236/1013","title":"Nonexistence of Permutation Binomials of Certain Shapes","year":2007,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":13,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Ottawa","funders":"","keywords":"Mathematics; Combinatorics; Permutation (music); Prime (order theory); Discrete 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":[0.003612566,0.00008861375,0.0002339817,0.0002044302,0.0000651813,0.00001636257,0.001087089,0.00004074458,0.00000377759],"category_scores_gemma":[0.0001025598,0.00006264055,0.000163208,0.0007510932,0.0000896437,0.0001857144,0.00006264477,0.0002755604,7.464643e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006900688,"about_ca_system_score_gemma":0.0002382238,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004316524,"about_ca_topic_score_gemma":0.00000212621,"domain_scores_codex":[0.9985683,0.0001311374,0.0005443587,0.00007989725,0.0003783943,0.0002979184],"domain_scores_gemma":[0.9981516,0.000500863,0.0007722385,0.0002185131,0.0003150059,0.00004178031],"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":[0.00006392328,0.00009513843,0.0002455844,0.00001231871,0.00004304717,0.000002430927,0.0008734456,0.0000771449,0.007260448,0.987244,0.00001363475,0.004068929],"study_design_scores_gemma":[0.0004945321,0.001034951,0.001942408,0.00003989846,0.00003290107,0.00008776315,0.0001969366,0.0004301319,0.03854773,0.9567903,0.0003173124,0.00008515417],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5928113,0.001524451,0.4044043,0.0002250995,0.0002079136,0.00005815151,2.436991e-7,0.000008404579,0.0007600333],"genre_scores_gemma":[0.9995555,0.0001611336,0.0002017359,0.00002522176,0.00002970569,3.068908e-7,7.854104e-8,0.000004799849,0.00002146152],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4067442,"threshold_uncertainty_score":0.2554408,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008703562126573168,"score_gpt":0.2421038410473745,"score_spread":0.2334002789208013,"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."}}