{"id":"W1968120658","doi":"10.1016/j.disc.2003.06.003","title":"Explicit enumeration of 321, hexagon-avoiding permutations","year":2003,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Enumeration; Mathematics; Generating function; Combinatorics; Recurrence relation; Simple (philosophy); Class (philosophy); Product (mathematics); Homogeneous space; Enumerative combinatorics; Term (time); Discrete mathematics; Computer science","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":[0.0008406558,0.0003483795,0.0006480799,0.0001624083,0.0002376744,0.00005261967,0.0003027004,0.0001455298,0.0001749612],"category_scores_gemma":[0.004930376,0.0003229527,0.0002084498,0.0004420175,0.00007942465,0.0002869013,0.00006353702,0.0002647189,0.00004930177],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009098037,"about_ca_system_score_gemma":0.00008030673,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002031445,"about_ca_topic_score_gemma":0.000002958065,"domain_scores_codex":[0.9974821,0.0001608323,0.001081458,0.0002980854,0.0005811881,0.0003963192],"domain_scores_gemma":[0.9965234,0.001585994,0.0006743901,0.0008322027,0.0002620022,0.0001219643],"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":[0.000003197482,0.0002597601,0.00002969284,0.0005574748,0.0000530234,0.000002475681,0.005699333,0.00004761814,0.005023558,0.9880319,0.0002252054,0.00006672023],"study_design_scores_gemma":[0.000501396,0.00006823592,0.000004291991,0.0002121064,0.0001176115,0.00002624665,0.004359076,0.001838302,0.0402666,0.9519354,0.0003328641,0.0003379367],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2803917,0.0001073416,0.688128,0.000079743,0.0004864408,0.000959846,0.00002955945,0.0002600401,0.02955739],"genre_scores_gemma":[0.7953555,0.00001358952,0.2037999,0.00001566999,0.00004957966,0.00007779217,0.000008433285,0.00009093915,0.0005886142],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.5149638,"threshold_uncertainty_score":0.9999223,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.050434782911579,"score_gpt":0.3357405044320268,"score_spread":0.2853057215204478,"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."}}