{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001658561,0.0006395378,0.0008343581,0.003723677,0.001344223,0.003098789,0.001515913,0.0008550052,0.003382073],"category_scores_gemma":[0.009784827,0.0004884923,0.000828644,0.001646857,0.003732148,0.004203787,0.001659038,0.001763424,0.0004222198],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002090391,"about_ca_system_score_gemma":0.000859751,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001977872,"about_ca_topic_score_gemma":0.001785947,"domain_scores_codex":[0.9990483,0.0003490804,0.00003878374,0.000117594,0.0002540813,0.0001921467],"domain_scores_gemma":[0.9962122,0.002190037,0.0005668707,0.0003048731,0.0003444874,0.0003814732],"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":[0.00007256101,0.00007651145,0.002098652,0.00005982182,0.00001633351,0.0002082901,0.0003231788,0.02106114,0.001462708,0.9700926,0.0004553616,0.004072762],"study_design_scores_gemma":[0.00003169776,0.00003819574,0.0009243188,0.00004516354,0.00001535322,0.000177992,0.0001977349,0.2773915,0.001395899,0.7187483,0.0009986919,0.00003514487],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8792038,0.0005573693,0.10006,0.0006931567,0.00004522603,0.00004200933,0.0001492612,0.0003041643,0.01894498],"genre_scores_gemma":[0.9853343,0.0002645999,0.0114124,0.0000595566,0.00005481972,0.00006611575,0.0001786232,0.00007183315,0.002557731],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003723677,"threshold_uncertainty_score":0.01516694,"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."}}