{"id":"W64760292","doi":"","title":"On Multi-Color Partitions with Distinct Parts.","year":2008,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Partition (number theory); Combinatorics; Colored; Discrete mathematics","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":[0.002034727,0.0009766839,0.001005659,0.0031484,0.001636876,0.002610248,0.001488305,0.001030251,0.004770418],"category_scores_gemma":[0.008732249,0.0005575747,0.0009862521,0.002741854,0.002943717,0.00549061,0.002449842,0.002116403,0.002415854],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002504095,"about_ca_system_score_gemma":0.0007127862,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001606868,"about_ca_topic_score_gemma":0.003159042,"domain_scores_codex":[0.9988085,0.0002539021,0.00007054474,0.000216427,0.0003249232,0.0003257582],"domain_scores_gemma":[0.9964529,0.00173826,0.0006528042,0.0005087007,0.0004255805,0.0002216678],"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":[0.0001336807,0.00002743192,0.001540203,0.0002028983,0.00001804063,0.0003430416,0.0009291468,0.003275636,0.005475982,0.9631021,0.003554544,0.02139724],"study_design_scores_gemma":[0.00003105569,0.00004824641,0.001929368,0.0001230479,0.00005032618,0.00133007,0.0002567655,0.03062595,0.008291546,0.9463088,0.01093878,0.00006602916],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4255668,0.008336327,0.402705,0.001958569,0.0009750785,0.0001991083,0.0009054791,0.001123197,0.1582305],"genre_scores_gemma":[0.9124684,0.002248597,0.05814873,0.0007342714,0.0003510079,0.0002865709,0.0005789128,0.0003690052,0.0248145],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004770418,"threshold_uncertainty_score":0.01816857,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05791716652199947,"score_gpt":0.3069946238129634,"score_spread":0.249077457290964,"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."}}