{"id":"W2094202793","doi":"10.1016/j.jctb.2004.08.003","title":"The perfect matching polytope and solid bricks","year":2004,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series B","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":27,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Polytope; Combinatorics; Mathematics; Matching (statistics); Perfect graph theorem; Birkhoff polytope; Convex hull; Convex polytope; Degree (music); Regular polygon; Discrete mathematics; Graph; Convex set; Line graph; Convex optimization; Geometry; Physics","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":[0.0030056,0.0001486592,0.0002523258,0.0001142492,0.0006073418,0.0004112221,0.001218304,0.00005637679,0.000005103502],"category_scores_gemma":[0.0004244182,0.0000963296,0.0001148739,0.0003128674,0.0003419219,0.001346984,0.0003589215,0.0005031619,0.000004425669],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007201483,"about_ca_system_score_gemma":0.0001868438,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000023483,"about_ca_topic_score_gemma":9.332391e-7,"domain_scores_codex":[0.9982305,0.0003867634,0.0003870201,0.0001543254,0.0004969357,0.0003444843],"domain_scores_gemma":[0.998183,0.0007257042,0.0002924698,0.0003834851,0.0002536904,0.0001617261],"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":[0.000361814,0.0000322938,0.00001937674,0.000004733272,0.00004038067,0.00005449399,0.0009776383,0.00008885445,0.001550767,0.9893067,0.00002419486,0.007538692],"study_design_scores_gemma":[0.0009794415,0.0006469293,0.0001349165,0.00003592668,0.000006708223,0.0005707818,0.0003584459,0.000006391151,0.006219813,0.9873368,0.003590032,0.0001137813],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6902145,0.004915585,0.2798334,0.006384028,0.01344885,0.0003963615,0.000001943167,0.0001214109,0.004683927],"genre_scores_gemma":[0.9965603,0.000345308,0.002433214,0.00008090173,0.000387907,0.000002021832,6.334675e-8,0.00001415036,0.0001761872],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3063458,"threshold_uncertainty_score":0.4671244,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008220812949512369,"score_gpt":0.2701819619439301,"score_spread":0.2619611489944177,"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."}}