{"id":"W2750023530","doi":"10.1007/978-3-319-66396-8_23","title":"Symmetric Dyck Paths and Hooley’s $$\\varDelta $$ Δ -Function","year":2017,"lang":"en","type":"book-chapter","venue":"Lecture notes in computer science","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Combinatorics; Lambda; Logarithm; Distribution (mathematics); Path (computing); Physics; Function (biology); Discrete mathematics; Mathematics; Mathematical analysis; Computer science; Quantum mechanics","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0008998632,0.0003994858,0.0005851655,0.0005290341,0.0002758388,0.0004232677,0.0007901986,0.0003533797,0.00006620956],"category_scores_gemma":[0.000811326,0.0003252119,0.0001011235,0.0001159735,0.0005472282,0.0001916873,0.0005746334,0.0006003201,0.0000324425],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001006103,"about_ca_system_score_gemma":0.000118168,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009887981,"about_ca_topic_score_gemma":0.0000367396,"domain_scores_codex":[0.9977121,0.00001530636,0.0004263289,0.0008045628,0.0006481783,0.0003935214],"domain_scores_gemma":[0.9973782,0.0009107185,0.0003782677,0.001029676,0.0001515512,0.0001516194],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000007356079,0.00004092268,0.00002907497,0.0002802672,0.00002181496,0.00003950958,0.0001771614,0.00008453199,0.00002320158,0.4683959,0.00006196138,0.5308383],"study_design_scores_gemma":[0.0001440467,0.0001017454,0.00007337056,0.0003937386,0.0000309522,0.00003151043,1.0183e-7,0.1281059,0.00001735261,0.8699641,0.0007855081,0.0003517353],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0002908663,0.0002726581,0.9706217,0.0002357293,0.0007366699,0.0003588219,0.00001256326,0.00006118666,0.02740981],"genre_scores_gemma":[0.5901852,0.0003402508,0.399297,0.001095779,0.001348476,0.00002505653,0.00001652409,0.0001944224,0.007497251],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.5898944,"threshold_uncertainty_score":0.99992,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0301977659359096,"score_gpt":0.2770450028871304,"score_spread":0.2468472369512208,"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."}}