{"id":"W43428214","doi":"","title":"A Bijective Proof of an Identity Concerning Nodes of Fixed Degree in Planted Trees.","year":2000,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Algebra and Logic","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Bijection; Degree (music); Identity (music); Combinatorics; Discrete mathematics; Aesthetics","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":[0.001848608,0.0008689985,0.001129149,0.001247423,0.003474765,0.002990697,0.002348283,0.002393688,0.01614403],"category_scores_gemma":[0.01072627,0.001126635,0.002155629,0.001663505,0.004042535,0.01376544,0.007389162,0.008343468,0.003541916],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001993489,"about_ca_system_score_gemma":0.001376719,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00215374,"about_ca_topic_score_gemma":0.003016618,"domain_scores_codex":[0.9983515,0.0004926346,0.0001026158,0.0003830071,0.0004378749,0.0002325102],"domain_scores_gemma":[0.9923368,0.004864551,0.0003214882,0.0009456804,0.0009760742,0.0005553786],"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":[0.00003141153,0.00006128019,0.0001950025,0.0001302158,0.00001694932,0.0001814121,0.0004854405,0.0004829124,0.001283388,0.9789523,0.009234648,0.008944913],"study_design_scores_gemma":[0.00001703563,0.00001453421,0.0002093726,0.00003578296,0.00002335924,0.0002800962,0.000128738,0.001542699,0.0008819776,0.9844688,0.0123779,0.00001966319],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04948552,0.002327858,0.7008578,0.008635935,0.003185441,0.0001961232,0.001261271,0.001516203,0.2325339],"genre_scores_gemma":[0.6786164,0.002970797,0.2294248,0.006912624,0.00222214,0.000572556,0.001604256,0.001918903,0.0757575],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01614403,"threshold_uncertainty_score":0.05400717,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02417275242599681,"score_gpt":0.2655721328022063,"score_spread":0.2413993803762095,"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."}}