{"id":"W2962755011","doi":"10.1007/s00493-018-3859-1","title":"Improved Bounds for Rota's Basis Conjecture","year":2018,"lang":"en","type":"article","venue":"COMBINATORICA","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Matroid; Combinatorics; Disjoint sets; Conjecture; Rank (graph theory); Basis (linear algebra); Discrete mathematics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.008853876,0.003980373,0.00553705,0.007124046,0.005755723,0.01158496,0.008505442,0.005776641,0.04708437],"category_scores_gemma":[0.04629451,0.00186697,0.003647562,0.007862682,0.009396739,0.02581637,0.01294238,0.01978611,0.01222705],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.006723432,"about_ca_system_score_gemma":0.00299104,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0034978,"about_ca_topic_score_gemma":0.003728616,"domain_scores_codex":[0.9899713,0.002847234,0.0003355115,0.001828652,0.003181283,0.00183605],"domain_scores_gemma":[0.9436323,0.04302379,0.001305251,0.006795049,0.003044088,0.002199591],"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":[0.0006916489,0.0002888148,0.001083513,0.0004912005,0.0000883134,0.0001892463,0.0005063315,0.009802677,0.001669772,0.9200491,0.03885343,0.02628604],"study_design_scores_gemma":[0.00005840305,0.00003168821,0.0002320406,0.0000836089,0.00005606324,0.0000723094,0.00007642757,0.02008775,0.0005852823,0.9730907,0.005589054,0.00003684155],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.1079473,0.01108429,0.3251802,0.04356127,0.004218134,0.0002927129,0.003880483,0.003594111,0.5002416],"genre_scores_gemma":[0.8149323,0.006529024,0.1018011,0.008985009,0.007291662,0.001172946,0.004093592,0.002491533,0.05270294],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.04708437,"threshold_uncertainty_score":0.1575129,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00628664731631921,"score_gpt":0.2029663673454901,"score_spread":0.1966797200291709,"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."}}