{"id":"W2540058515","doi":"10.46298/dmtcs.3599","title":"Delannoy numbers and Legendre polytopes","year":2008,"lang":"en","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":"York University","funders":"","keywords":"Mathematics; Polytope; Combinatorics; Legendre polynomials; Quadrant (abdomen); Triangulation; Humanities; Geometry; Mathematical analysis","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":[0.0002220773,0.000432899,0.000357813,0.00103011,0.0009725532,0.001352194,0.0004875171,0.0002891653,0.008643724],"category_scores_gemma":[0.0009354348,0.0002415981,0.0004955296,0.0005264731,0.00206133,0.001256352,0.001505701,0.00108837,0.0009432161],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008262033,"about_ca_system_score_gemma":0.0003758402,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001287777,"about_ca_topic_score_gemma":0.001675717,"domain_scores_codex":[0.9997037,0.00003255221,0.000009614251,0.00008215936,0.00008366867,0.00008822672],"domain_scores_gemma":[0.9994612,0.0001351417,0.0001254887,0.00008416385,0.00008405364,0.0001100181],"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":[0.0001081341,0.00003343702,0.00149183,0.00009873617,0.000008618777,0.0002019095,0.0002918523,0.009852313,0.01390256,0.9469368,0.001665539,0.02540835],"study_design_scores_gemma":[0.00009415733,0.000383437,0.007609823,0.0001212402,0.00003310763,0.001518998,0.001371242,0.09458049,0.03527995,0.8029616,0.0559093,0.0001366764],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6759067,0.0004805782,0.2424783,0.0003389154,0.0001305396,0.00006553141,0.0003043749,0.0003386334,0.07995637],"genre_scores_gemma":[0.9084412,0.0004233018,0.06743857,0.00008538035,0.00006609636,0.0001079191,0.0004200771,0.0001248657,0.02289264],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008643724,"threshold_uncertainty_score":0.02891612,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02331329170674692,"score_gpt":0.2916541476952403,"score_spread":0.2683408559884934,"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."}}