{"id":"W4402679330","doi":"10.1007/s11083-024-09685-7","title":"Partition Rank and Partition Lattices","year":2024,"lang":"en","type":"article","venue":"Order","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"","keywords":"Mathematics; Partition (number theory); Combinatorics; Rank (graph theory); Discrete mathematics; Algebra over a field; Pure mathematics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00199672,0.0008428082,0.001681532,0.005171179,0.003485312,0.007176742,0.001254394,0.001757761,0.01315467],"category_scores_gemma":[0.01057593,0.0009136595,0.0007230999,0.004020116,0.006194475,0.01082829,0.002642,0.00372809,0.001117243],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00195937,"about_ca_system_score_gemma":0.001395304,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002078921,"about_ca_topic_score_gemma":0.002216662,"domain_scores_codex":[0.9981601,0.0006405582,0.00006539753,0.000314293,0.0005316327,0.0002879473],"domain_scores_gemma":[0.987012,0.007947561,0.001402191,0.001246814,0.001194217,0.001197217],"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":[0.00002243598,0.00001491981,0.00009633409,0.00001639865,0.000003321927,0.00001283578,0.0001086974,0.001133555,0.0001004481,0.9953674,0.001123293,0.002000337],"study_design_scores_gemma":[0.000007571065,0.000006440001,0.00007595376,0.000007914012,0.000003804768,0.00002812507,0.00005928952,0.005793794,0.0001105488,0.9927102,0.001188263,0.000008073681],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.442371,0.004209663,0.3571452,0.01169,0.0006507849,0.0001434934,0.001695182,0.0006382981,0.1814564],"genre_scores_gemma":[0.9366702,0.001566491,0.02584226,0.000914641,0.0009097989,0.0001260013,0.0006236936,0.0002221912,0.03312467],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01315467,"threshold_uncertainty_score":0.04400671,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006325592644393327,"score_gpt":0.2001727517342348,"score_spread":0.1938471590898414,"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."}}