{"id":"W3186837486","doi":"10.46298/dmtcs.10296","title":"The Variance and the Asymptotic Distribution of the Length of Longest $k$-alternating Subsequences","year":2023,"lang":"en","type":"article","venue":"Discrete Mathematics & Theoretical Computer Science","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Longest increasing subsequence; Permutation (music); Random permutation; Combinatorics; Subsequence; Statistic; Variance (accounting); Limit (mathematics); Distribution (mathematics); Statistics; Symmetric group; Mathematical analysis; Bounded function","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":[0.003536689,0.0006191615,0.0007361998,0.001996537,0.0004972634,0.001710521,0.001864482,0.001002878,0.00636168],"category_scores_gemma":[0.03226379,0.0004988432,0.0007989274,0.00120579,0.003101269,0.003708165,0.001617025,0.00229422,0.001621866],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009885116,"about_ca_system_score_gemma":0.0008562673,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008191504,"about_ca_topic_score_gemma":0.0006982683,"domain_scores_codex":[0.9979407,0.0004744826,0.0001157021,0.0006915163,0.0005179329,0.0002595491],"domain_scores_gemma":[0.9835149,0.01113703,0.001383989,0.001854493,0.001617649,0.0004919867],"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":[0.0003075085,0.0001278607,0.01106255,0.0004096199,0.0001365261,0.00071985,0.0004868928,0.08679753,0.03294234,0.8080285,0.003598858,0.05538213],"study_design_scores_gemma":[0.00004230039,0.0001317682,0.01199921,0.0001935838,0.00006258024,0.001262898,0.0001656104,0.4601538,0.01088611,0.5110126,0.003914032,0.0001754127],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1636778,0.001429359,0.8209968,0.0009623523,0.0002221164,0.00006909708,0.0005150011,0.0005918131,0.01153584],"genre_scores_gemma":[0.911548,0.001637868,0.07602796,0.0003254056,0.0005283798,0.0003200296,0.001055743,0.0004871688,0.008069419],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00636168,"threshold_uncertainty_score":0.02128196,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01804998310482082,"score_gpt":0.2883338550758182,"score_spread":0.2702838719709973,"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."}}