{"id":"W2740563568","doi":"10.46298/dmtcs.3597","title":"A generalization of $(q,t)$-Catalan and nabla operators","year":2008,"lang":"fr","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Fields Institute for Research in Mathematical Sciences; York University","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Nabla symbol; Mathematics; Schur algebra; Combinatorics; Operator (biology); Schur's lemma; Generalization; Commutative property; Pure mathematics; Orthogonal polynomials; Mathematical analysis; Classical orthogonal polynomials; Omega","routes":{"ca_aff":true,"ca_fund":true,"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":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.001817643,0.0006226288,0.001097488,0.0003089283,0.0006752046,0.0001907805,0.001274671,0.0002545678,0.0001859371],"category_scores_gemma":[0.001388784,0.0005565978,0.0001823528,0.00141978,0.01199499,0.0007174971,0.001232067,0.0003915306,0.00004802597],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001237638,"about_ca_system_score_gemma":0.0002999408,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006353555,"about_ca_topic_score_gemma":8.384934e-7,"domain_scores_codex":[0.9951148,0.0001962376,0.00141853,0.0008465246,0.001462936,0.0009609546],"domain_scores_gemma":[0.9956765,0.001127104,0.0006038989,0.001346814,0.0006942115,0.0005515145],"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":[0.0000102053,0.0004619973,0.00005032021,0.001166525,0.00004261774,0.00003116692,0.01032399,0.00008597858,0.00110394,0.9858362,0.0001265035,0.0007605656],"study_design_scores_gemma":[0.0005090766,0.0003024829,0.00002112868,0.0006898237,0.000113195,0.0003754253,0.0002191399,0.2595623,0.006916718,0.7306855,0.0001022318,0.0005029067],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2437431,0.0006590173,0.7500885,0.0005154395,0.001306042,0.00073606,0.00003758257,0.0001069634,0.002807278],"genre_scores_gemma":[0.5360384,0.0002054168,0.4631896,0.00006344915,0.0002039735,0.00001561353,0.000003936998,0.00007006832,0.0002095349],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.2922953,"threshold_uncertainty_score":0.9996886,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01862875044457815,"score_gpt":0.2777405158156227,"score_spread":0.2591117653710446,"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."}}