{"id":"W2011862520","doi":"10.1006/jcta.2000.3090","title":"Noncommutative Pieri Operators on Posets","year":2000,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series A","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":54,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"","keywords":"Hopf algebra; Mathematics; Representation theory of Hopf algebras; Noncommutative geometry; Symmetric function; Morphism; Algebra over a field; Eulerian path; Partially ordered set; Pure mathematics; Cellular algebra; Symmetric algebra; Quasitriangular Hopf algebra; Filtered algebra; Division algebra; Combinatorics; Algebra representation; Lagrangian","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":[0.002056399,0.001860306,0.001503963,0.005200507,0.004981901,0.00849164,0.001620726,0.00196138,0.01385063],"category_scores_gemma":[0.003187384,0.001735202,0.001719619,0.004730463,0.006824769,0.0165001,0.006639386,0.00580245,0.001656033],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001913171,"about_ca_system_score_gemma":0.0008713751,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004029198,"about_ca_topic_score_gemma":0.0006422807,"domain_scores_codex":[0.9978915,0.0004230101,0.0001383276,0.0003754937,0.0006795977,0.0004920842],"domain_scores_gemma":[0.9975369,0.0008935651,0.0003848104,0.0002734824,0.0002422063,0.0006690164],"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":[0.00001483683,0.00001971746,0.00007141323,0.00001026001,0.000003413842,0.000114765,0.0003110011,0.0001214297,0.0004225336,0.9976531,0.0003106202,0.0009468311],"study_design_scores_gemma":[0.00001241071,0.0000182442,0.0001620962,0.000006948951,0.000006894025,0.0002583815,0.0002339817,0.0007560758,0.0004853031,0.9958211,0.002221489,0.00001694022],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6017916,0.001485936,0.1413435,0.003992519,0.001673825,0.0001313388,0.000443745,0.0004707688,0.2486668],"genre_scores_gemma":[0.9173585,0.0009634462,0.01594259,0.000688889,0.00123038,0.0001342897,0.0003003814,0.000243907,0.06313751],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01385063,"threshold_uncertainty_score":0.04633498,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01910019330812778,"score_gpt":0.3076467139488878,"score_spread":0.28854652064076,"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."}}