{"id":"W2963299469","doi":"10.1016/j.jctb.2013.09.007","title":"The number of rank- k flats in a matroid with no<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:msub><mml:mrow><mml:mi>U</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math>-minor","year":2014,"lang":"lv","type":"article","venue":"Journal of Combinatorial Theory Series B","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Office of Naval Research","keywords":"Matroid; Rank (graph theory); Minor (academic); Combinatorics; Mathematics; Prime power; Prime (order theory); Art","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":["metaepi_narrow","sts","scholarly_communication","research_integrity","insufficient_payload"],"consensus_categories":["metaepi_narrow","sts","research_integrity","insufficient_payload"],"category_scores_codex":[0.009348658,0.001286709,0.0007849802,0.0008576573,0.002089683,0.00218143,0.004189436,0.002958163,0.3783657],"category_scores_gemma":[0.007288542,0.002105054,0.002660297,0.001815249,0.003693747,0.002624826,0.002662947,0.003714393,0.002224039],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000453668,"about_ca_system_score_gemma":0.002837466,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006900159,"about_ca_topic_score_gemma":0.000758947,"domain_scores_codex":[0.9843467,0.002112262,0.003630213,0.001700136,0.004839614,0.00337106],"domain_scores_gemma":[0.9829723,0.006796923,0.004769718,0.003235868,0.000707208,0.001517968],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.01368558,0.0006758481,0.00002802725,0.00184809,0.002651877,0.001513499,0.003542051,0.0004347891,0.002567959,0.7598732,0.2120043,0.001174804],"study_design_scores_gemma":[0.006761211,0.00576523,0.00007136316,0.002891193,0.002116932,0.003903536,0.004721248,0.005560117,0.9367417,0.0222011,0.007114993,0.002151341],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5597438,0.0009896909,0.0003974801,0.0005885998,0.005705942,0.00007336878,0.0001961221,0.0001387283,0.4321663],"genre_scores_gemma":[0.9881707,0.001507756,0.002267408,0.0007794984,0.00431819,0.0007025526,0.0002681028,0.001225219,0.0007605428],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9341738,"threshold_uncertainty_score":0.9999885,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01607873139706964,"score_gpt":0.2519183165433745,"score_spread":0.2358395851463048,"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."}}