{"id":"W4205800876","doi":"10.1016/j.jctb.2010.08.001","title":"On inequivalent representations of matroids over non-prime fields","year":2010,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series B","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Matroid; Prime (order theory); Combinatorics; Finite field; Mathematics; Order (exchange); Mace; Graphic matroid; Field (mathematics); Discrete mathematics; Pure 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001509608,0.0009165027,0.0009975268,0.002375469,0.002430785,0.005308037,0.001576599,0.002344728,0.01330197],"category_scores_gemma":[0.004298992,0.0006555423,0.001008864,0.002118584,0.003239221,0.008360157,0.002909932,0.003826371,0.001057623],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00170969,"about_ca_system_score_gemma":0.0004805147,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000563166,"about_ca_topic_score_gemma":0.0009434094,"domain_scores_codex":[0.9985876,0.0004082141,0.0001048525,0.0002033599,0.0003510425,0.0003448935],"domain_scores_gemma":[0.9973302,0.001196494,0.0003905054,0.0003659452,0.0002903538,0.0004265133],"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":[0.00006076194,0.0000577521,0.0002480593,0.00002380435,0.000004763639,0.0001186058,0.0003649145,0.0005370102,0.0006372315,0.9924649,0.0007884807,0.004693847],"study_design_scores_gemma":[0.00001913542,0.00001771613,0.0001537952,0.00001390869,0.000005526912,0.0001071478,0.0002060226,0.002602278,0.0002566841,0.9955481,0.001061353,0.000008277057],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8128921,0.0008585592,0.05779073,0.003283585,0.000638581,0.00009850881,0.0003811921,0.0002360367,0.1238207],"genre_scores_gemma":[0.9681007,0.0005525735,0.01262204,0.0004842447,0.0004383895,0.00005998199,0.0004530873,0.000146725,0.01714227],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01330197,"threshold_uncertainty_score":0.04449952,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009937836447893521,"score_gpt":0.3008611600237114,"score_spread":0.2909233235758178,"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."}}