{"id":"W2963224836","doi":"","title":"Asymptotics of lattice walks via analytic combinatorics in several variables","year":2016,"lang":"en","type":"article","venue":"HAL (Le Centre pour la Communication Scientifique Directe)","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Generating function; Hermite polynomials; Lattice (music); Combinatorics; Diagonal; Enumerative combinatorics; Algebraic number; Rational function; Discrete mathematics; Pure mathematics; Mathematical analysis","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":[],"consensus_categories":[],"category_scores_codex":[0.003847803,0.0002420364,0.0004724331,0.0001961695,0.0001010659,0.00004227035,0.0007570258,0.0001648362,0.00008542071],"category_scores_gemma":[0.006716045,0.0002071182,0.00011331,0.0007012506,0.0001862966,0.000235596,0.0003289143,0.0002058153,0.00002180203],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001952427,"about_ca_system_score_gemma":0.0001202278,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008279978,"about_ca_topic_score_gemma":0.000175074,"domain_scores_codex":[0.9965291,0.001494148,0.0007697298,0.000370946,0.0004662522,0.000369825],"domain_scores_gemma":[0.9897735,0.006798949,0.0005336456,0.001434348,0.001333581,0.0001259423],"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":[0.000009063446,0.0007295184,0.001281669,0.0001425195,0.00003459127,0.000003412816,0.00197537,0.000008697986,0.002520214,0.990685,0.0001246334,0.002485282],"study_design_scores_gemma":[0.001363595,0.000001239169,0.0005045972,0.001140664,0.00004739089,0.000008472206,0.00006758825,0.005673765,0.03452373,0.9557791,0.000603623,0.000286266],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1999849,0.0001019357,0.7712964,0.002068983,0.0002622377,0.0004144875,0.00001740013,0.000174172,0.02567952],"genre_scores_gemma":[0.8800203,0.00006994993,0.116871,0.00001719726,0.00001012969,0.00001657272,0.000006338712,0.00004777944,0.002940681],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6800354,"threshold_uncertainty_score":0.8446033,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01608249019305455,"score_gpt":0.2488170826424357,"score_spread":0.2327345924493811,"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."}}