{"id":"W1706968406","doi":"10.46298/dmtcs.2825","title":"Combinatorial formulas for double parabolic R-polynomials","year":2010,"lang":"fr","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Hecke algebra; Polynomial; Pure mathematics; Simple (philosophy); Combinatorics; Computation; Algebra over a field; Mathematical analysis; Algorithm; Philosophy","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":[0.0005793309,0.0004567883,0.0004300298,0.001748114,0.001242559,0.00377426,0.001160026,0.0007639319,0.007236863],"category_scores_gemma":[0.002773883,0.0004499961,0.0007888197,0.001991766,0.002735231,0.006749892,0.001589762,0.001757405,0.0007688092],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001838459,"about_ca_system_score_gemma":0.0005927902,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001250438,"about_ca_topic_score_gemma":0.001413438,"domain_scores_codex":[0.9993625,0.0001024649,0.00004711024,0.0001415851,0.000260182,0.00008618608],"domain_scores_gemma":[0.9988666,0.0004662756,0.0002079231,0.0001552554,0.0002199843,0.0000840987],"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":[0.0000124726,0.000008757048,0.0002684904,0.00003531265,0.000002355945,0.0001654397,0.0003378968,0.0004647731,0.0008416348,0.9935323,0.0004175222,0.003913042],"study_design_scores_gemma":[0.00001377618,0.00001713828,0.0005200586,0.00002560104,0.00001394934,0.0004314094,0.0003627485,0.005669781,0.001644182,0.9825907,0.008684193,0.00002646251],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5598397,0.001788522,0.2674586,0.002423143,0.0002970187,0.000119377,0.0005748892,0.0003566674,0.1671419],"genre_scores_gemma":[0.9256438,0.001099137,0.04786678,0.0003274545,0.000239892,0.00009245628,0.000315842,0.0001234102,0.02429115],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007236863,"threshold_uncertainty_score":0.02420974,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01856170029092127,"score_gpt":0.2948552762722648,"score_spread":0.2762935759813435,"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."}}