{"id":"W102350756","doi":"","title":"Binomial Identities Generated by Counting Spanning Trees.","year":2007,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Spanning tree; Binomial (polynomial); Combinatorics; Statistics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001216592,0.0004613342,0.0008040372,0.002631479,0.001821285,0.002581981,0.001059137,0.0009792504,0.01238033],"category_scores_gemma":[0.008215332,0.0004484904,0.0006931475,0.001750291,0.001527826,0.003788915,0.002261825,0.00194643,0.003006095],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009081803,"about_ca_system_score_gemma":0.0005774958,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005400983,"about_ca_topic_score_gemma":0.0009446479,"domain_scores_codex":[0.9987144,0.0003792165,0.00006493949,0.0001689301,0.000442926,0.0002296422],"domain_scores_gemma":[0.9967931,0.001662927,0.0003718065,0.0002775301,0.0005146725,0.0003799915],"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":[0.0000226416,0.00001672636,0.0002668759,0.00002963838,0.000004977087,0.0001298974,0.0001311971,0.000340215,0.0006700634,0.9881054,0.003403387,0.006878887],"study_design_scores_gemma":[0.00001341926,0.000008801671,0.0003228103,0.00002639931,0.00001340473,0.0004514693,0.00006413672,0.008180111,0.000774285,0.9839566,0.006176259,0.00001223904],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3078917,0.001736705,0.3223695,0.002766247,0.001751098,0.000135666,0.0009619266,0.0006464922,0.3617407],"genre_scores_gemma":[0.8840978,0.001108255,0.05162919,0.0007809158,0.001206998,0.0001809394,0.0008942896,0.000324826,0.05977678],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01238033,"threshold_uncertainty_score":0.04141635,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0157873052285918,"score_gpt":0.277797935104111,"score_spread":0.2620106298755193,"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."}}