{"id":"W1969959148","doi":"10.1007/s00026-011-0095-4","title":"Enumerative Properties of NC (B) (p,q)","year":2011,"lang":"en","type":"article","venue":"Annals of Combinatorics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Combinatorics; Partially ordered set; Generating function; Type (biology); Rank (graph theory); Möbius function; Lattice (music); Discrete mathematics; 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":[0.0004273112,0.0002140555,0.0005954369,0.0001203874,0.0000470725,0.000004669295,0.0004112786,0.0001174225,0.00003684901],"category_scores_gemma":[0.001246588,0.0001854808,0.0001516752,0.000368468,0.0001840564,0.00021068,0.0001308397,0.0001558243,0.000009169266],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000136243,"about_ca_system_score_gemma":0.00006929376,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001530418,"about_ca_topic_score_gemma":9.356173e-7,"domain_scores_codex":[0.998312,0.00008855531,0.0007281321,0.0001761654,0.0004299025,0.0002652524],"domain_scores_gemma":[0.9975445,0.0002164156,0.0006451664,0.0005793596,0.0009345494,0.00007997527],"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":[0.00005470355,0.0008480672,0.0002164061,0.000447279,0.00008454623,0.000002644199,0.004402807,4.400748e-7,0.001612915,0.9915596,0.0005994652,0.0001711505],"study_design_scores_gemma":[0.0002317799,0.0002353686,0.00004205102,0.0001238357,0.0000210544,0.000001582698,0.0002140384,0.00001269064,0.3746819,0.6241881,0.0001276059,0.0001199866],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9687753,0.000641462,0.003361718,0.00008832722,0.000788859,0.0005516223,0.000009918725,0.0001145631,0.02566823],"genre_scores_gemma":[0.9956079,0.000077745,0.003922346,0.00002419829,0.00002024922,0.0000201087,5.226694e-7,0.000039517,0.0002874404],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.373069,"threshold_uncertainty_score":0.7563687,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.4083369210621418,"score_gpt":0.3648739633036224,"score_spread":0.04346295775851938,"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."}}